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    Wyświetlanie 1-8 z 8
    Tytuł:
    Maximal stability bounds of discrete-time singularly perturbed systems
    Autorzy:
    Chen, S.-J
    Lin, J.-L.
    Powiązania:
    https://bibliotekanauki.pl/articles/970412.pdf
    Data publikacji:
    2004
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    discrete-time singularly perturbed system
    stability bound
    eigenvalue loci
    Kronecker product of LFTs
    Opis:
    The exact stability bound of the parasitic parameter for a discrete-time singularly perturbed system is determined by the linear fractional transformation (LFT) framework. Two systematic approaches including time-domain and frequency-domain methods are proposed to solve this problem based on the unified LFT framework. One employs the Kronecker product of LFTs and the guardian map theory. The other is to plot the eigenvalue loci of a real rational function matrix. Two examples are given to show the feasibility of the approaches.
    Źródło:
    Control and Cybernetics; 2004, 33, 1; 95-108
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Diagnosis of discrete-time singularly perturbed systems based on slow subsystem
    Autorzy:
    Tellili, A.
    Abdelkrim, N.
    Jaouadi, B.
    Abdelkrim, M. N.
    Powiązania:
    https://bibliotekanauki.pl/articles/386452.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    discrete-time singularly perturbed system
    two time scales property
    model based fault diagnosis
    parity space approach
    slow subsystem
    układ dyskretny
    diagnozowanie uszkodzeń
    podsystem
    Opis:
    This paper deals with the diagnosis of discrete-time singularly perturbed systems presenting two time scales property. Parity space method is considered to generate the fault detection residual. The focus is in two directions. First, we discuss the residual illconditioning caused by the singular perturbation parameter. Then, the use of the slow subsystem is considered to make the fault diagnosis easier. It is shown that the designed diagnostic algorithm based on reduced order model is close to the one synthesized using the full order system. The developed approach aims at reducing the computational load and the ill-conditioning for stiff residual generation problem. Two examples of application are used to demonstrate the efficiency of the proposed method.
    Źródło:
    Acta Mechanica et Automatica; 2014, 8, 4; 175-180
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability of nominally stable uncertain singularly perturbed systems with multiple time delays
    Autorzy:
    Chen, C.
    Pan, S.
    Hsieh, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/206124.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    stabilność asymptotyczna
    asymptotic stability
    delay-dependent criterion
    singularly perturbed system
    Opis:
    In this paper, the robust asymptotic stability problem for a class of nominally stable uncertain singularly perturbed systems with multiple non-commensurate time delays is considered. A delay-dependent criterion is first proposed in this paper to guarantee robust asymptotic stability of the system under consideration. Based on this result, the range of allowable bounds of the perturbation matrices preserving the closed-loop stability can easily be found. Moreower, a simple criterion is also proposed to guarantee asymptotic, stability of the nominal system. Furthermore, a simple estimation of the stability bound epsilon* is proposed such that the nominal system is asymptotically stable for epsilon [belongs to](0,epsilon*). It can be seen that the stability bound proposed in this paper is less conservative than that presented in recent research. Finally, a numerical example is provided to illustrate our main results.
    Źródło:
    Control and Cybernetics; 2002, 31, 1; 5-16
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A simple criterion for the global exponential stability of uncertain T-S fuzzy singularly perturbed discrete-time systems
    Autorzy:
    Sun, Y. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205643.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Takagi-Sugeno fuzzy system
    singularly perturbed systems
    uncertain systems
    Opis:
    In this paper, the global exponential stability for a class of uncertain Takagi-Sugeno (T-S) fuzzy singularly perturbed systems is investigated. Based on time-domain approach with difference inequality technique, a simple criterion is derived to guarantee the global exponential stability of such systems. The upper bound of the singular perturbation parameter is also provided by estimating the unique positive zero of specific function. Finally, two numerical examples are given to demonstrate the feasibility and effectiveness of the obtained result.
    Źródło:
    Control and Cybernetics; 2011, 40, 1; 59-71
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Diffusion limit for the phenomenon of random genetic drift
    Autorzy:
    Marciniak, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/1208221.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    genetic drift
    telegraph equations
    singularly perturbed systems
    diffusion equation
    random walk
    Opis:
    The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as the telegraph equations). Applying the modified Chapman-Enskog procedure we show the transition from this system to a macroscopic model which is a diffusion type equation. Finally, the error of approximation is estimated.
    Źródło:
    Applicationes Mathematicae; 2000, 27, 1; 81-101
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Correctness of a constrained control Mayers problem for a class of singularly perturbed functional-differential systems
    Autorzy:
    Glizer, V. Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/969600.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    functional differential system
    time delay
    Mayer's problem
    bounded control
    singular perturbation
    correctness
    suboptimal control
    Opis:
    A Mayer's problem for a singularly perturbed controlled system with the general type of a small state delay is considered. The control is subject to geometrical constraints. The cost functional is a function of the terminal value of the slow state variable. A simpler parameter-free optimal control problem (the reduced problem) is associated with the original problem. A convergence of the optimal value of the cost functional in the original problem to the optimal value of the cost functional in the reduced problem, as a parameter of singular perturbation tends to zero, is established. An asymptotic suboptimality of the optimal control of the reduced problem in the original problem is shown. These results are extended to some more general optimal control problems. An illustrative example is presented.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 329-351
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Algorithm for solution of systems of singularly perturbed differential equations with adifferential turning point
    Autorzy:
    Sobchuk, Valentyn
    Zelenska, Iryna
    Laptiev, Oleksandr
    Powiązania:
    https://bibliotekanauki.pl/articles/27311440.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    singular perturbations
    asymptotics
    Airy-Langer functions
    small parameter
    turning points
    punkt zwrotny
    funkcje Airy'ego-Langera
    asymptota
    perturbacja singularna
    parametr niski
    Opis:
    The dynamic development of science requires constant improvement of approaches to modeling physical processes and phenomena. Practically all scientific problems can be described by systems of differential equations. Many scientific problems are described by systems of differential equations of a special class, which belong to the group of so-called singularly perturbed differential equations. Mathematical models of processes described by such differential equations contain a small parameter near the highest derivatives, and it was the presence of this small factor that led to the creation of a large mathematical theory. The work proposes a developed algorithm for constructing uniform asymptotics of solutions to systems of singularly perturbed differential equations.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 3; art. no. e145682
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Shape and topology optimization of distributed parameter systems
    Autorzy:
    Sokołowski, J.
    Żochowski, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/206802.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    shape optimization
    topological derivative
    asymptotic analysis
    singularly perturbed geometrical domains
    asymptotic expansion of energ functional
    Opis:
    The energy functional for an elliptic boundary value problem in two spatial dimensions is considered. The variations of shape functional resulting from the small shape-topological domain perturbations with the holes and inclusions in elastic body are determined. The exact representation of solutions to the boundary value problem is exploited for the purposes of asymptotic analysis. To this end the perturbed solutions of the boundary value problem are Expressem as the minimizers of perturbed energy functionals. The proposed method of asymptotic analysis results in the double asymptotic expansions, with respect to the size of a hole and to the contrast parameter of an inclusion with respect to the matrix, of solutions to the boundary value problems as well as of the associated energy functional. The shape sensitivity analysis of the energy functional with respekt of the boundary variations of an inclusion is performed. The further asymptotic analysis allows for the limit passage with the size of inclusion to zero. In this way the topological derivative of the energy functional is obtained. The proposed analysis can be used in the shape and topology optimum design for elastic bodies governed by the stationary as well as by the time dependent elasticity boundary value problems in the framework of selfadjoint extensions of elliptic operators.
    Źródło:
    Control and Cybernetics; 2013, 42, 1; 217-226
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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