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Wyświetlanie 1-15 z 35
Tytuł:
Analysis of positive linear continuous-time systems using the conformable derivative
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/331153.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
conformable fractional derivative
positive linear system
system stability
pochodna ułamkowa
układ liniowy dodatni
stabilność systemu
Opis:
Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2018, 28, 2; 335-340
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:
Simple conditions for practical stability of positive fractional discrete-time linear systems
Autorzy:
Busłowicz, M.
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/907662.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system liniowy
system dyskretno-czasowy
system ułamkowy
stateczność
stateczność praktyczna
linear system
positive
discrete-time
fractional
stability
practical stability
Opis:
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 263-269
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
Autorzy:
Ostalczyk, P.
Powiązania:
https://bibliotekanauki.pl/articles/330106.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
rachunek ułamkowy
system dyskretno-czasowy
system liniowy
fractional calculus
linear-discrete time system
stability domain
Opis:
Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 3; 533-538
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems
Autorzy:
Busłowicz, M.
Ruszewski, A.
Powiązania:
https://bibliotekanauki.pl/articles/331316.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
układ ciągło-dyskretny
system hybrydowy
metoda komputerowa
continuous-discrete system
hybrid system
stability
computer methods
Opis:
Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 401-408
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Delay-dependent Asymptotic Stabilitzation for Uncertain Time-delay Systems with Saturating Actuators
Autorzy:
Liu, P. L.
Powiązania:
https://bibliotekanauki.pl/articles/908496.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
stabilność
system opóźniania
równanie Riccatiego
stability
delay-dependency
time delay system
Riccati equation
Opis:
This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2005, 15, 1; 45-51
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Absolute stability of a class of fractional positive nonlinear systems
Autorzy:
Kaczorek, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/331023.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
absolute stability
fractional system
positive system
nonlinear system
stabilność absolutna
układ ułamkowy
układ dodatni
układ nieliniowy
Opis:
The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2019, 29, 1; 93-98
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local analysis of hybrid systems on polyhedral sets with state-dependent switching
Autorzy:
Leth, J.
Wisniewski, R.
Powiązania:
https://bibliotekanauki.pl/articles/330556.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
inkluzja różniczkowa
badanie stabilności
układ hybrydowy
stability analysis
switched system
hybrid system
differential inclusion
Opis:
This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 341-355
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global stability of nonlinear feedback systems with fractional positive linear parts
Autorzy:
Kaczorek, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/330048.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
global stability
fractional positive system
nonlinear system
feedback system
stateczność globalna
układ ułamkowy
układ dodatni
układ nieliniowy
Opis:
The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1,−1/k2).
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 3; 493-499
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global stability of discrete-time feedback nonlinear systems with descriptor positive linear parts and interval state matrices
Autorzy:
Kaczorek, Tadeusz
Ruszewski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/2055149.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
global stability
positive system
nonlinear system
discrete-time system
stabilność globalna
układ dodatni
układ nieliniowy
układ czasu dyskretnego
Opis:
The global stability of discrete-time nonlinear systems with descriptor positive linear parts, positive scalar feedbacks and interval state matrices is addressed. Sufficient conditions for the global stability of this class of nonlinear systems are established. The effectiveness of these conditions is illustrated using numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2022, 32, 1; 5--10
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A modified van der Pol equation with delay in a description of the heart action
Autorzy:
Zduniak, B.
Bodnar, M.
Foryś, U.
Powiązania:
https://bibliotekanauki.pl/articles/330034.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system with feedback
stability
action potential
sprzężenie zwrotne
stabilność
potencjał czynnościowy
Opis:
In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage of certain values for feedback and delay parameters allows simulating the heart action when an accessory conducting pathway is present (Wolff–Parkinson–White syndrome).
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 853-863
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linear Repetitive Process Control Theory Applied to a Physical Example
Autorzy:
Gałkowski, K.
Rogers, E.
Paszke, W.
Owens, D. H.
Powiązania:
https://bibliotekanauki.pl/articles/908259.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
automatyka
robotyka
repetitive dynamics
metal rolling
LMIs
delay differential system
stability
Opis:
In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward translation into efficient routinely applicable controller design algorithms for applications domains. In this paper, we introduce the dynamics of these processes by outlining the development of models for various metal rolling operations. These models are then used to illustrate some recent results on the development of a comprehensive control theory for these processes.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 1; 87-99
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of interval positive fractional discrete-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/331118.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
interval system
positive system
fractional system
linear discrete-time system
stability
system przedziałowy
układ dodatni
układ ułamkowy
układ liniowy
układ dyskretno-czasowy
Opis:
The aim of this work is to show that interval positive fractional discrete-time linear systems are asymptotically stable if and only if the respective lower and upper bound systems are asymptotically stable. The classical Kharitonov theorem is extended to interval positive fractional linear systems.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2018, 28, 3; 451-456
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
Autorzy:
Grzymkowski, Łukasz
Trofimowicz, Damian
Stefański, Tomasz P.
Powiązania:
https://bibliotekanauki.pl/articles/1838161.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
stability analysis
discrete time system
fractional order system
analiza stabilności
układ czasu dyskretnego
układ rzędu ułamkowego
Opis:
In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained theoretical results lead to a numerical test for stability evaluation of interconnected FO systems. It is based on modern root-finding techniques on the complex plane employing triangulation of the unit circle and Cauchy’s argument principle. The developed numerical test is simple, intuitive and can be applied to a variety of systems. Furthermore, because it evaluates the function related to the characteristic equation on the complex plane, it does not require computation of state-matrix eigenvalues. The obtained numerical results confirm the efficiency of the developed test for the stability analysis of interconnected discrete-time FO LTI state-space systems.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 649-658
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 35

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