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    Wyświetlanie 1-49 z 49
    Tytuł:
    Positivity and stability of fractional 2D Lyapunov systems described by the Roesser model
    Autorzy:
    Rogowski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/202275.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    positive system
    stability
    fractional 2D system
    Lyapunov system
    Roesser model
    Opis:
    A new class of fractional 2D Lyapunov systems described by the Roesser models is introduced. Necessary and sufficient conditions for the positivity and asymptotic stability of the new class of systems are established. It is shown that the checking of the asymptotic stability of positive 2D fractional Lyapunov systems can be reduced to testing the asymptotic stability of corresponding positive standard 1D discretetime systems. The considerations are illustrated by a numerical example.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2011, 59, 2; 195-200
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov matrices approach to the parametric optimization of a neutral system
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229256.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    neutral system
    Lyapunov matrix
    Lyapunov functional
    Opis:
    In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system. The Lyapunov functional is determined by means of the Lyapunov matrix.
    Źródło:
    Archives of Control Sciences; 2016, 26, 1; 81-93
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov matrices approach to the parametric optimization of a system with two delays and a PD-controller
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229274.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    neutral system
    Lyapunov matrix
    Lyapunov functional
    Opis:
    In the paper the parametric optimization problem for a linear system with two delays and a PD-controller is presented. In the parametric optimization problem the quadratic performance index is considered. The value of the quadratic index of quality is calculated due to the Lyapunov functional and is equal to the value of that functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix.
    Źródło:
    Archives of Control Sciences; 2018, 28, 4; 585-600
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov matrices approach to the parametric optimization of time-delay systems
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229179.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time-delay system
    Lyapunov matrix
    Lyapunov functional
    Opis:
    In the paper a Lyapunov matrices approach to the parametric optimization problem of timedelay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.
    Źródło:
    Archives of Control Sciences; 2015, 25, 3; 279-288
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Lyapunov functional for a system with both lumped and distributed delay
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229640.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time-delay system
    Lyapunov matrix
    Lyapunov functional
    Opis:
    In the paper construction of a Lyapunov functional for time delay system with both lumped and distributed delay is presented. The Lyapunov functional is determined by means of the Lyapunov matrix. The method of determination of the Lyapunov matrix for time delay system with both lumped and distributed delay is presented. It is given the example illustrating the method.
    Źródło:
    Archives of Control Sciences; 2017, 27, 4; 527-540
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The parametric optimization of a system with two delays and a PI controller
    Autorzy:
    Duda, Jozef
    Powiązania:
    https://bibliotekanauki.pl/articles/229717.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time-delay system
    Lyapunov matrix
    Lyapunov functional
    Opis:
    In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.
    Źródło:
    Archives of Control Sciences; 2019, 29, 4; 667-686
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229975.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time-delay system
    Lyapunov matrix
    Lyapunov functional
    Opis:
    In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with two commensurate delays and a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of the Lyapunov functional for the initial function of time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.
    Źródło:
    Archives of Control Sciences; 2016, 26, 3; 367-381
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov functional for a linear system with both lumped and distributed delay
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205647.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Lyapunov functional
    time delay system
    LTI system
    Opis:
    The paper presents a method of determining the Lyapunov quadratic functional for linear tirne-invariant system with both lumped and distributed delay. The Lyapunov functional is constructed for its given time derivative, which is calculated on the trajectory of the system with both lumped and distributed delay. The method presented gives analytical formulas for the coefficients of the Lyapunov functional.
    Źródło:
    Control and Cybernetics; 2011, 40, 1; 73-90
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov functional for a linear system with two delays
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/969912.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Lyapunov functional
    time delay system
    LTI system
    Opis:
    The paper presents a method of determining the Lyapunov functional for linear time-invariant LTI system with two lumped delays.
    Źródło:
    Control and Cybernetics; 2010, 39, 3; 797-809
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov functional for a linear system with two delays both retarded and neutral type
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229843.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Lyapunov functional
    time delay system
    LTI system
    Opis:
    The paper presents a method of determining of the Lyapunov quadratic functional for linear time-invariant system with two delays both retarded and neutral type. The Lyapunov functional is constructed for a given its time derivative which is calculated on the trajectory of the system with two delays both retarded and neutral type. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
    Źródło:
    Archives of Control Sciences; 2010, 20, 1; 89-98
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the stability of continuous-time positive switched systems with rank one difference
    Autorzy:
    Fornasini, E.
    Valcher, M. E.
    Powiązania:
    https://bibliotekanauki.pl/articles/971053.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    switched system
    positive linear system
    asymptotic stability
    linear copositive Lyapunov function quadratic Lyapunov function
    Opis:
    Continuous-time positive systems, switching among p subsystems whose matrices differ by a rank one matrix, are introduced, and a complete characterization of the existence of a common linear copositive Lyapunov function for all the subsystems is provided. Also, for this class of systems it is proved that a well-known necessary condition for asymptotic stability, namely the fact that All convex combinations of the system matrices are Hurwitz, becomes equivalent to the generally weaker condition that the systems matrices are Hurwitz. In the special case of two-dimensional systems, this allows for drawing a complete characterization of asymptotic stability. Finally, the case when there are only two subsystems, possibly with commuting matrices, is investigated.
    Źródło:
    Control and Cybernetics; 2013, 42, 1; 47-62
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lyapunov functional for a system with k-non-commensurate neutral time delays
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/970175.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Lyapunov functional
    time delay system
    neutral system
    LTI system
    Opis:
    The paper presents a method of determining the Lyapunov quadratic functional for linear time-invariant system with k-non-commensurate neutral type time delays. The Lyapunov functional is constructed for its given time derivative, which is calculated on the trajectory of the system with k-non-commensurate neutral type time delays. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
    Źródło:
    Control and Cybernetics; 2010, 39, 4; 1173-1184
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fault detection based on Lyapunov exponents estimation for stabilized mechanical systems
    Autorzy:
    Puzyrov, Volodymyr
    Acho, Leonardo
    Pujol, Gisela
    Rodellar, José
    Powiązania:
    https://bibliotekanauki.pl/articles/281447.pdf
    Data publikacji:
    2019
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    fault detection
    switched system
    Lyapunov characteristic exponent
    underactuated system
    Opis:
    We study a stabilizable mechanical system in the vicinity of an equilibrium position. This position, as a rule, is unstable, and the system is underactuated. It is assumed that faults affect the technical process and its control. We suggest a fault diagnosis technique based on estimation of Lyapunov characteristic exponents of measured variables. A model of a linear switching system is involved for the system with faults description, and a common quadratic Lyapunov function is used to evaluate the deviation of the maximum exponent with respect to the default system. A scheme of fault magnitude estimation is suggested related to the degree of this deviation. An example of a 2-degree of freedom system is presented to illustrate the procedure.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2019, 57, 2; 519-531
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Parametric optimization of a neutral system with two delays and PD-controller
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229662.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    parametric optimization
    Lyapunov functional
    time delay system
    neutral system
    Opis:
    In this paper a parametric optimization problem for a linear neutral system with two delays with an integral quadratic performance index is formulated and solved. The method of computing of a performance index value bases on determining of a Lyapunov functional defined on a state space such that its value for an initial state is equal to a performance index value. In the paper a form of a Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of discussed theory is presented. It concerns the system with a PD-controller designed to control a plant with two delays both retarded and neutral type. For such system a value of considered performance index is determined.
    Źródło:
    Archives of Control Sciences; 2013, 23, 2; 131-143
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Parametric optimization of neutral linear system with two delays with P-controller
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/229977.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    parametric optimization
    Lyapunov functional
    time delay system
    neutral system
    Opis:
    In the paper the problem of parametric optimization of a linear neutral system with two delays accomplished with respect to the integral quadratic performance index is formulated and solved. A method of computing the value of performance index relies on determining such a Lyapunov functional defined on the state space that its value for the initial state is equal to that of performance index. In the paper the form of Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of the theory discussed is presented. It concerns a system with the P-controller designed to control a plant with two delays both retarded and neutral type. For such a system the value of the considered performance index is determined.
    Źródło:
    Archives of Control Sciences; 2011, 21, 4; 363-372
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Lyapunov functional for a neutral system with a time-varying delay
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/200885.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Lyapunov functional
    time-varying delay
    neutral system
    Opis:
    The paper presents a method of determining of the Lyapunov functional for a linear neutral system with an interval time-varying delay. The Lyapunov functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the trajectory of the system with a time-varying delay. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 4; 911-918
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Lyapunov functional for a system with a time-varying delay
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/331415.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    funkcjonał Lapunowa
    system opóźniania
    Lyapunov functional
    time delay system
    LTI system
    Opis:
    The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval time-varying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 327-337
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Global rational stabilization of a class of nonlinear time-delay systems
    Autorzy:
    Echi, Nadhem
    Ghanmi, Boulbaba
    Powiązania:
    https://bibliotekanauki.pl/articles/229187.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    rational stability
    delay system
    nonlinear observer
    Lyapunov functional
    Opis:
    The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.
    Źródło:
    Archives of Control Sciences; 2019, 29, 2; 259-278
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Synchronization of fractional order Rabinovich-Fabrikant systems using sliding mode control techniques
    Autorzy:
    Kumar, Sanjay
    Singh, Chaman
    Prasad, Sada Nand
    Shekhar, Chandra
    Aggarwal, Rajiv
    Powiązania:
    https://bibliotekanauki.pl/articles/229902.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional-order chaotic system
    chaos synchronization
    Rabinovich-Fabrikant system
    Lyapunov exponents
    Opis:
    In this research article, we present the concepts of fractional-order dynamical systems and synchronization methodologies of fractional order chaotic dynamical systems using slide mode control techniques. We have analysed the different phase portraits and time-series graphs of fractional order Rabinovich-Fabrikant systems. We have obtained that the lowest dimension of Rabinovich-Fabrikant system is 2.85 through utilization of the fractional calculus and computational simulation. Bifurcation diagrams and Lyapunov exponents of fractional order Rabinovich-Fabrikant system to justify the chaos in the systems. Synchronization of two identical fractional-order chaotic Rabinovich-Fabrikant systems are achieved using sliding mode control methodology.
    Źródło:
    Archives of Control Sciences; 2019, 29, 2; 307-322
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Funkcjonały Lapunowa dla układów z opóźnieniem
    Lyapunov functionals for time delay systems
    Autorzy:
    Duda, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/274656.pdf
    Data publikacji:
    2011
    Wydawca:
    Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
    Tematy:
    funkcjonał Lapunowa
    układy z opóźnieniem
    Lyapunov functional
    time delay system
    Opis:
    W pracy przedstawiono zastosowanie funkcjonałów Lapunowa do badania stabilności układów z opóźnieniem oraz w procesie optymalizacji parametrycznej.
    In the paper was presented the application of the Lyapunov functionals to examination of the stability of the time delay systems and in the process of parametric optimization.
    Źródło:
    Pomiary Automatyka Robotyka; 2011, 15, 12; 64-65
    1427-9126
    Pojawia się w:
    Pomiary Automatyka Robotyka
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of positivity and stability of time-varying continuous-time linear systems and electrical circuits
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/97265.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
    Tematy:
    positive
    linear
    time-varying
    system
    electrical circuit
    stability
    Lyapunov method
    test
    Opis:
    The positivity and stability of a class of time-varying continuous-time linear systems and electrical circuits are addressed. Sufficient conditions for the positivity and asymptotic stability of the system are established. It is shown that there exists a large class of positive and asymptotically stable electrical circuits with time-varying parameters. The Lyapunov method is extended to positive nonlinear systems. Examples of positive electrical circuits are presented.
    Źródło:
    Computer Applications in Electrical Engineering; 2015, 13; 1-18
    1508-4248
    Pojawia się w:
    Computer Applications in Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Serworegulator dla klasy ciągłych układów nieliniowych
    Servocontroller for a class of nonlinear continuous-time system
    Autorzy:
    Kurek, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/277676.pdf
    Data publikacji:
    2010
    Wydawca:
    Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
    Tematy:
    układ nieliniowy
    serworegulator
    metoda Lapunowa
    nonlinear system
    servo controller
    Lyapunov method
    Opis:
    W pracy przedstawiono serworegulator dla klasy nieliniowych ciągłych układów o zmiennych w czasie parametrach z niemierzalnym ograniczonym zakłóceniem. Regulator może być zastosowany do regulacji niepewnych układów liniowych. Do syntezy układu regulacji wykorzystano drugą metodę Lapunowa.
    Servocontroller for a class of nonlinear time-varying continuous-time systems with unmeasurable bounded disturbances is presented. The controller can be also used for control of uncertain nonlinear systems. The second Lyapunov stability theorem has been applied for synthesis of stable control system.
    Źródło:
    Pomiary Automatyka Robotyka; 2010, 14, 11; 52-53
    1427-9126
    Pojawia się w:
    Pomiary Automatyka Robotyka
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Extending Lyapunov redesign method for robust stabilization of non-affine quadratic polynomial systems
    Autorzy:
    Binazadeh, T.
    Rahgoshay, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/205649.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Lyapunov redesign
    non-affine
    quadratic polynomial systems
    magnetic ball levitation system
    Opis:
    The Lyapunov redesign method is basically used for robust stabilization of nonlinear systems with an affine structure. In this paper, for the first time, by suggestion of a simple but effective idea, this approach is developed for robust stabilization of non-affine quadratic polynomial systems in the presence of uncertainties and external disturbances. In the proposed method, according to the upper bound of an uncertain term, a quadratic polynomial is constructed and with respect to the position of the roots of this polynomial, the additional feedback law is designed for robustness of the quadratic polynomial system. The proposed technique is also used for robust stabilizing of a magnetic ball levitation system. When the coil current is the control input of the magnetic ball levitation system, equations of this system are increasingly nonlinear with respect to control input and have quadratic polynomial structure. The effectiveness of the proposed control law is also demonstrated through computer simulations.
    Źródło:
    Control and Cybernetics; 2016, 45, 3; 373-384
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Synchronization of neuronal bursting using backstepping control with recursive feedback
    Autorzy:
    Rasappan, Suresh
    Powiązania:
    https://bibliotekanauki.pl/articles/229893.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Hindmarsh-Rose neuronal bursting system
    chaos
    synchronization
    backstepping control
    Lyapunov
    stability
    Opis:
    J. L. Hindmarsh, R. M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.
    Źródło:
    Archives of Control Sciences; 2019, 29, 4; 617-642
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of a common solution to the Lyapunov equations
    Autorzy:
    Białas, S.
    Góra, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/201354.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    common quadratic Lyapunov functions
    switched system
    robust stability
    funkcje kwadratowe Lapunowa
    system przełączników
    wysoka stabilność
    Opis:
    In this paper, a system of Lyapunov equations A*i P + PAi = −Qi (i = 1, . . . ,m), (A) is considered in which Ai are given n × n complex matrices, Qi are unknown n × n Hermitian positive definite matrices and P, if any, is a common solution to the Lyapunov equations (A). Both sufficient and necessary and sufficient conditions are derived for the existence of such a matrix P. Examples are presented to illustrate the results.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 1; 163--168
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability of a class of adaptive nonlinear systems
    Autorzy:
    Dzieliński, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/908445.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system nieliniowy
    stabilność Lapunova
    układ adaptacyjny
    nonlinear systems
    Lyapunov stability
    adaptive systems
    Opis:
    This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2005, 15, 4; 455-462
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tracking and disturbance rejection in a nonlinear control system with time delay
    Autorzy:
    Chien, T.-L.
    Chen, C.-C.
    Wu, C.-J.
    Huang, Y.-C.
    Chen, C.-Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/969741.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    disturbance rejection
    automobile idle-speed control system
    differential geometry approach
    composite Lyapunov approach
    Opis:
    We consider the problem of designing a feedback control law in order to reject the unknown bounded disturbance and achieve tracking of reference inputs in control systems described by a class of nonlinear time-delay differential-algebraic equations. Based on the input-output feedback linearization technique and Lya-pimov method for nonlinear state feedback synthesis, a robust globally asymptotical output tracking controller design methodology for nonlinear time-delay control systems with delays on the states and the input is developed. The underlying theoretical approaches are the differential geometry approach and the composite Lyapunov approach. For the view of practical application, the proposed control methodology has been successfully applied to the famous nonlinear automobile idle-speed control system problem.
    Źródło:
    Control and Cybernetics; 2007, 36, 1; 59-74
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Adaptive backstepping tracking control for an over-actuated DP marine vessel with inertia uncertainties
    Autorzy:
    Witkowska, A.
    Śmierzchalski, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/331460.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    over actuated control
    adaptive control
    Lyapunov function
    control allocation
    MIMO system
    sterowanie adaptacyjne
    funkcja Lapunowa
    system MIMO
    Opis:
    Designing a tracking control system for an over-actuated dynamic positioning marine vessel in the case of insufficient information on environmental disturbances, hydrodynamic damping, Coriolis forces and vessel inertia characteristics is considered. The designed adaptive MIMO backstepping control law with control allocation is based on Lyapunov control theory for cascaded systems to guarantee stabilization of the marine vessel position and heading. Forces and torque computed from the adaptive control law are allocated to individual thrusters by employing the quadratic programming method in combination with the cascaded generalized inverse algorithm, the weighted least squares algorithm and the minimal least squares algorithm. The effectiveness of the proposed control scheme is demonstrated by simulations involving a redundant set of actuators. The evaluation criteria include energy consumption, robustness, as well accuracy of tracking during typical vessel operation.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2018, 28, 4; 679-693
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis, adaptive control and circuit simulation of a novel finance system with dissaving
    Autorzy:
    Tacha, O. I.
    Volos, C. K.
    Stouboulos, I. N.
    Kyprianidis, I. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/229959.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    chaotic finance system
    dissaving
    bifurcation diagram
    Lyapunov exponent
    phase portrait
    adaptive control
    nonlinear circuit
    Opis:
    In this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called ‘dissaving’ is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system’s behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.
    Źródło:
    Archives of Control Sciences; 2016, 26, 1; 95-115
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    ℎ-Stability of set differential equations
    Autorzy:
    Boukthir, Sihem
    Ghanmi, Boulbaba
    Basdouri, Imed
    Ichalal, Dalil
    Lerbet, Jean
    Powiązania:
    https://bibliotekanauki.pl/articles/27324010.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    ℎ-stability
    Lyapunov theory
    set-valued differential
    generalized Hukuhara derivative
    perturbed system
    cascaded systems
    Opis:
    In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems.
    Źródło:
    Archives of Control Sciences; 2023, 33, 4; 761--788
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Robust output feedback Model Predictive Control design
    Autorzy:
    Vesely, V.
    Rosinova, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/229853.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    model predictive control
    robust control
    parameter dependent quadratic stability
    Lyapunov functional
    polytopic system
    decentralized control
    Opis:
    The paper addresses the problem of designing a robust output/state model predictive control for linear polytopic systems without constraints. The new robust BMI stability condition for given predictive and control horizon is derived which guarantees the parameter dependent quadratic stability and guaranteed cost.The proposed condition is appropriate for centralized and decentralized control design, as illustrated on example.
    Źródło:
    Archives of Control Sciences; 2010, 20, 3; 303-316
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Robust output predictive sequential controller design
    Autorzy:
    Vesely, V.
    Rosinova, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/229887.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    model predictive control
    robust control
    parameter dependent quadratic stability
    Lyapunov function
    polytopic system
    sequential approach
    Opis:
    The paper addresses design problem of a robust parameter dependent quadratically stabilizing output/state feedback model predictive control for linear polytopic systems without constraints using original equential approach. The design procedure ensures stability, robustness properties and guaranteed cost for the closed-loop uncertain system
    Źródło:
    Archives of Control Sciences; 2010, 20, 1; 31-46
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fundamental limitations of the decay of generalized energy in controlled (discrete-time) nonlinear systems subject to state and input constraints
    Autorzy:
    Selek, István
    Ikonen, Enso
    Powiązania:
    https://bibliotekanauki.pl/articles/330074.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    decay rate maximization
    Lyapunov function
    nonlinear control system
    rozkład wykładniczy
    funkcja Lapunowa
    układ sterowania nieliniowy
    Opis:
    This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 4; 629-639
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Improved fuzzy feedback linearization and Sinswat-transformation control of inverted pendulum
    Autorzy:
    Chien, T. L.
    Chen, C. C.
    Chen, Y. C.
    Wu, S. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/970222.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    fuzzy logic control
    almost disturbance decoupling
    feedback linearization approach
    composite Lyapunov approach
    inverted pendulum control system
    Opis:
    This paper studies the output tracking and almost disturbance decoupling problem of nonlinear control systems with uncertainties via fuzzy logic control and feedback linearization approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system enjoys for any initial condition and bounded tracking signal the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling, i.e., the influence of disturbances on the L2 norm of the output tracking error can be arbitrarily attenuated by increasing some adjustable parameters. The underlying theoretical approaches are the differential geometry approach and the composite Lyapunov approach. One example, which cannot be solved by the approach from the first paper (Marino et al., 1989) on the almost disturbance decoupling problem, is proposed in this paper to exploit the fact that the almost disturbance decoupling and the convergence rate performances are easily achieved by virtue of our approach. In order to demonstrate the practical applicability, the paper takes up the study of an inverted pendulum control system.
    Źródło:
    Control and Cybernetics; 2010, 39, 4; 1069-1093
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sharply-weak regular linear extensions of dynamical systems leading up to regular systems
    Dopełnienie słabo regularnych liniowych rozszerzeń układów dynamicznych do układów regularnych
    Autorzy:
    Tkocz-Piszczek, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/87345.pdf
    Data publikacji:
    2011
    Wydawca:
    Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
    Tematy:
    rozszerzenie liniowe
    układ dynamiczny
    równanie różniczkowe
    funkcja Lapunowa
    linear extension
    dynamical system
    differential equation
    Lyapunov function
    Opis:
    In this paper we consider some sign–changing Lyapunov function in research on regularity and sharply-week regularity of sets of linear extensions of dynamical systems. By regularity we mean exponential dichotomy of linear differential systems.
    Wartykule podjęto tematykę regularności liniowych rozszerzeń układów dynamicznych, która równoważna jest z wykładniczą dychotomią liniowych układów różniczkowych. Przeprowadzono badanie regularności przy użyciu znakozmiennych funkcji Lapunowa. Ponadto, przedstawiono doprowadzenie słabo regularnych układów do regularnych.
    Źródło:
    Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska; 2011, 1; 51-68
    2084-073X
    Pojawia się w:
    Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability and positivity with respect to part of the variables for positive Markovian jump systems
    Autorzy:
    Socha, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/200593.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    hybrid system
    Lyapunov method
    Markov jump systems
    stability and positivity with respect to the part of variables
    Opis:
    The stability and positivity of linear positive Markovian jump systems with respect to part of the variables is considered. The method-ologies of stability of positive systems with known transition probabilities based on common linear copositive Lyapunov function and stability of linear systems with respect to part of the variables are combined to find sufficient conditions of the stochastic stability and positivity of Markovian jump systems with respect to part of the variables. The results are extended for a class of nonlinear positive Markovian jump systems with respect to part of the variables. An example is given to illustrate the obtained results.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 4; 769-775
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law
    Autorzy:
    Ouannas, Adel
    Mesdoui, Fatiha
    Momani, Shaher
    Batiha, Iqbal
    Grassi, Giuseppe
    Powiązania:
    https://bibliotekanauki.pl/articles/1409370.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    FitzHugh-Nagumo
    synchronization
    uni-dimensional control
    linear control
    reaction-diffusion system
    neuronal networks
    Lyapunov’s second method
    Opis:
    The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.
    Źródło:
    Archives of Control Sciences; 2021, 31, 2; 333-345
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    PD terminal sliding mode control using fuzzy genetic algorithm for mobile robot in presence of disturbances
    Autorzy:
    Benaziza, W.
    Slimane, N.
    Mallem, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/384371.pdf
    Data publikacji:
    2018
    Wydawca:
    Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
    Tematy:
    mobile robot
    fast terminal function
    PD sliding surface
    fuzzy system
    genetic algorithm
    Lyapunov stability
    robot mobilny
    system rozmyty
    algorytm genetyczny
    Stabilność Lapunova
    Opis:
    This paper presents a new approach in the field of trajectory tracking for nonholonomic mobile robot in presence of disturbances. The proposed control design is constructed by a kinematic controller, based on PD sliding surface using fuzzy sliding mode for the angular and linear velocities disturbances, in order to tend asymptotically the robot posture error to zero. Thereafter a dynamic controller is presented using as a sliding surface design, a fast terminal function (FTF) whose parameters are generated by a genetic algorithm in order to converge the velocity errors to zero in finite time and guarantee the asymptotic stability of the system using a Lyapunov candidate. The elaborated simulation works in the case of different trajectories confirm the robustness of the proposed approach.
    Źródło:
    Journal of Automation Mobile Robotics and Intelligent Systems; 2018, 12, 2; 52-60
    1897-8649
    2080-2145
    Pojawia się w:
    Journal of Automation Mobile Robotics and Intelligent Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On potential kernels associated with random dynamical systems
    Autorzy:
    Hmissi, M.
    Mokchaha, F.
    Hmissi, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1397853.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dynamical system
    random dynamical systems
    random differential equations
    stochastic differential equation
    potential kernel
    domination principle
    Lyapunov function
    Opis:
    Let $(\Theta;, \phi)$ be a continuous random dynamical system defined on a probability space $(\Omega, F, P)$ and taking values on a locally compact Hausdorff space E. The associated potential kernel V is given by $V f(\omega, x) = \int_0^\infty f (\Theta_t \omega, \phi(t, \omega)x)dt, \omega \in \Omega, x \in E$. In this paper, we prove the equivalence of the following statements: 1. The potential kernel of $(\Theta, \phi)$ is proper, i.e. $V f$ is x-continuous for each bounded, x-continuous function with uniformly random compact support. 2. $(\Theta, \phi)$ has a global Lyapunov function, i.e. a function $ L : \Omega \times E \rightarrow (0, \infty) $ which is x-continuous and $ L(\Theta_t\omega, \phi(t,\omega)x) \downarrow 0$ as $ t \uparrow \infty $. In particular, we provide a constructive method for global Lyapunov functions for gradient-like random dynamical systems. This result generalizes an analogous theorem known for deterministic dynamical systems.
    Źródło:
    Opuscula Mathematica; 2015, 35, 4; 499-515
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    T–S fuzzy BIBO stabilisation of non-linear systems under persistent perturbations using fuzzy Lyapunov functions and non-PDC control laws
    Autorzy:
    Salcedo, José V.
    Martínez, Miguel
    García-Nieto, Sergio
    Hilario, Adolfo
    Powiązania:
    https://bibliotekanauki.pl/articles/330030.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    linear matrix inequalities
    Takagi–Suegno fuzzy system
    fuzzy Lyapunov function
    integral delayed Lyapunov function
    nonparallel distributed fuzzy controller
    generalised inescapable ellipsoids
    liniowe nierówności macierzowe
    model rozmyty Takagi-Sugeno
    funkcja Lapunowa
    Opis:
    This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi–Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum ⋆-norm (upper bound of the 1-norm) for the T–S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 3; 529-550
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Stability Interval of the Set of Linear System
    Autorzy:
    Mazakov, Talgat
    Wójcik, Waldemar
    Jomartova, Sholpan
    Karymsakova, Nurgul
    Ziyatbekova, Gulzat
    Tursynbai, Aisulu
    Powiązania:
    https://bibliotekanauki.pl/articles/1844628.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    automatic control system
    stability
    matrix
    minor
    characteristic polynomial
    Hurwitz criterion
    Lienard-Shipard criterion of interval mathematics
    Lyapunov function
    Opis:
    The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and LienardShipar interval criteria. Krylov, Leverier, and Leverier-Danilevsky algorithms are implemented for automated construction and analysis of the interval characteristic polynomial. The interval mathematics library was used while developing the software. The stability of the dynamic system described by linear ordinary differential equations is determined and based on the properties of the eigenvalues of the interval characteristic polynomial. On the basis of numerical calculations, the authors compare several methods of constructing the characteristic polynomial. The developed software that implements the introduced interval arithmetic operations can be used in the study of dynamic properties of automatic control systems, energy, economic and other non-linear systems.
    Źródło:
    International Journal of Electronics and Telecommunications; 2021, 67, 2; 155-161
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalized practical stability analysis of discontinuous dynamical systems
    Autorzy:
    Zhai, G.
    Michel, A. N.
    Powiązania:
    https://bibliotekanauki.pl/articles/907305.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ dynamiczny nieciągły
    analiza ilościowa
    funkcja Lyapunova
    discontinuous dynamical system
    quantitative analysis
    generalized practical stability
    Lyapunov-like function
    Opis:
    In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and establish some sufficient conditions concerning GP-stability for a wide class of discontinuous dynamical systems. As in the classical Lyapunov theory, our results constitute a Direct Method, making use of auxiliary scalar-valued Lyapunov-like functions. These functions, however, have properties that differ significantly from the usual Lyapunov functions. We demonstrate the applicability of our results by means of several specific examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 1; 5-12
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Simple environment for developing methods of controlling chaos in spatially distributed systems
    Autorzy:
    Korus, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/907826.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    stabilność układu
    wykładnik Lapunowa
    metoda Lyapunova
    coupled map lattice
    spatiotemporal chaos
    system stability
    Lyapunov exponents
    net direction phase
    Opis:
    The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of its parameters, this model generates complex, spatiotemporal behavior which seems to be chaotic. The main purpose of the paper is to provide results of stability analysis and compare them with those obtained from numerical simulation. The indirect Lyapunov method and Lyapunov exponents are used to examine the dependence on initial conditions. The net direction phase is introduced to measure the symmetry of the system state trajectory. In addition, a real system, which can be modeled by the CML, is presented. In general, this article describes basic elements of environment, which can be used for creating and examining methods of chaos controlling in systems with spatiotemporal dynamics.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 1; 149-159
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior
    Autorzy:
    Korus, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/331175.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    controlling spatiotemporal chaos
    coupled map lattice
    system stability
    Lyapunov exponent
    net direction phase
    stabilność układu
    wykładnik Lapunowa
    kierunek fazy
    Opis:
    The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 759-770
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On three methods for bounding the rate of convergence for some continuous-time Markov chains
    Autorzy:
    Zeifman, Alexander
    Satin, Yacov
    Kryukova, Anastasia
    Razumchik, Rostislav
    Kiseleva, Ksenia
    Shilova, Galina
    Powiązania:
    https://bibliotekanauki.pl/articles/329966.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    inhomogeneous continuous time Markov chains
    weak ergodicity
    Lyapunov function
    differential inequalities
    forward Kolmogorov system
    łańcuchy Markowa z czasem ciągłym
    funkcja Lapunowa
    nierówność różniczkowa
    system Kołmogorowa
    Opis:
    Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/S queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared with those known from the literature) under which the methods are applicable are being formulated. Two numerical examples are given. It is also shown that, for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 2; 251-266
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modeling nonlinear road traffic networks for junction control
    Autorzy:
    Péter, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/330975.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    modelowanie matematyczne
    układ dodatni nieliniowy
    liniowa funkcja Lapunowa
    mathematical modeling
    mathematical control
    traffic networks
    nonlinear positive system
    linear Lyapunov function
    Opis:
    The paper introduces a method of mathematical modeling of high scale road traffic networks, where a new special hypermatrix structure is intended to be used. The structure describes the inner-inner, inner-outer and outer-outer relations, and laws of a network area. The research examines the nonlinear equation system. The analysed model can be applied to the testing and planning of large-scale road traffic networks and the regulation of traffic systems. The elaborated model is in state space form, where the states are vehicle densities on a particular lane and the dynamics are described by a nonlinear state constrained positive system. This model can be used directly for simulation and analysis and as a starting point for investigating various control strategies. The stability of the traffic over the network can be analyzed by constructing a linear Lyapunov function and the associated theory. The model points out that in intersection control one must take the traffic density values of both the input and the output sections into account. Generally, the control of any domain has to take the density of input and output sections into consideration.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 3; 723-732
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Badanie hybrydowego układu napędowego wg stabilności Lapunowa
    Testing the hybrid powertrain by Lyapunovs stability theory
    Autorzy:
    Banaś, W.
    Kost, G.
    Nierychlok, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/408909.pdf
    Data publikacji:
    2011
    Wydawca:
    Politechnika Śląska
    Tematy:
    hybrydowy układ napędowy
    MATLAB/Simulink
    pojazd kołowy
    metoda Lapunowa
    stabilność
    hybrid drive system
    MATLAB Simulink
    wheeled vehicle
    Lyapunov method
    stability
    Opis:
    W pracy przedstawiono model pojazdu kołowego o napędzie hybrydowym zbudowanym w oprogramowaniu MATLAB/Simulink. W modelu przyjęto założenia sterowania silnikiem spalinowym jako maszyną napędzającą pojazd kołowy i generator elektryczny. Takie podejście wymaga zbadania stabilności układu napędowego, w którym silnik spalinowy raz będzie napędzał tylko i wyłącznie generator elektryczny, zaś w innym przypadku tylko i wyłącznie pojazd kołowy. Sprawa komplikuje się jeszcze bardziej w chwili wspomagania silnika elektrycznego silnikiem spalinowym (synergia energii). Dlatego w pracy podjęto próbę opisu układu napędowego pojazdu kołowego równaniami różniczkowymi, a następnie zbadania stabilności takiego układu w sensie Lapunowa.
    The paper presents a model of a hybrid wheeled vehicle built in the Matlab/Simulink software. In the model controlling by a combustion engine as a driving unit of wheeled vehicle and an electric generator were assumed. Such approach requires an examination of the stability of the propulsion system for which an internal combustion engine will power once and only an electric generator, while in other case only the wheeled vehicle. The case is more complicated when the electric motor is supported by the combustion engine (Synergy Energy). Therefore, the study attempts to describe the propulsion system of a wheeled vehicle by differential equations and then to examine the stability of such system in the sense of Lyapunov's theory were undertaken.
    Źródło:
    Wybrane Problemy Inżynierskie; 2011, 2; 23-28
    2083-1021
    Pojawia się w:
    Wybrane Problemy Inżynierskie
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties
    Autorzy:
    Balasubramaniam, P.
    Lakshmanan, S.
    Rakkiyappan, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/331417.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    opóźnienie zależne
    liniowa nierówność macierzowa
    system stochastyczny
    stabilność odporna
    delay-dependent stability
    linear matrix inequality
    Lyapunov-Krasovskii functional
    stochastic systems
    Opis:
    This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 339-351
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    J-energy preserving well-posed linear systems
    Autorzy:
    Staffans, O. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/908123.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ zachowawczy
    system liniowy
    równanie Lyapunova
    równanie różniczkowe Riccatiego
    well-posed linear systems
    system node
    transfer function
    Lax-Phillips semigroup
    dissipative systems
    conservative system
    model theory
    conservative realization
    J-energy-preserving system
    Lyapunov equations
    Riccati equation
    Opis:
    The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE's, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foias. The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems (H2- and Hinfty-theories).
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1361-1378
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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