Journal ArticleDOI
Disturbance Attenuation Properties of Time-Controlled Switched Systems
TLDR
This paper investigates the disturbance attenuation properties of time-controlled switched systems consisting of several linear time-invariant subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function and shows that if the total activation time of unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, then a reasonable weighted disturbance attenuations level is guaranteed.Abstract:
In this paper, we investigate the disturbance attenuation properties of time-controlled switched systems consisting of several linear time-invariant subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than a positive scalar γ0, the switched system under an average dwell time scheme achieves a weighted disturbance attenuation level γ0, and the weighted disturbance attenuation approaches normal disturbance attenuation if the average dwell time is chosen sufficiently large. We extend this result to the case where not all subsystems are Hurwitz stable, by showing that in addition to the average dwell time scheme, if the total activation time of unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, then a reasonable weighted disturbance attenuation level is guaranteed. Finally, a discussion is made on the case for which nonlinear norm-bounded perturbations exist in the subsystems.read more
Citations
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Journal ArticleDOI
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
Hai Lin,Panos J. Antsaklis +1 more
TL;DR: This paper focuses on the stability analysis for switched linear systems under arbitrary switching, and highlights necessary and sufficient conditions for asymptotic stability.
Journal ArticleDOI
Stability and L2-gain analysis for switched delay systems: A delay-dependent method
TL;DR: Sufficient conditions for exponential stability and weighted L"2-gain are developed for a class of switching signals with average dwell time and these conditions are given in the form of linear matrix inequalities (LMIs).
Journal ArticleDOI
On stability, L2-gain and H∞ control for switched systems
Jun Zhao,David J. Hill +1 more
TL;DR: In this article, a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized Lyapunov-like functions, which enables derivation of improved stability tests, an L"2-gain characterization and a design method for stabilizing switching laws.
Journal ArticleDOI
Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time
Lixian Zhang,Peng Shi +1 more
TL;DR: The stability and l 2-gain problems for a class of discrete-time switched systems with average dwell time (ADT) switching are investigated by allowing the Lyapunov-like functions to increase during the running time of subsystems to facilitate the studies on the issue of asynchronous control.
Journal ArticleDOI
Dissipativity Theory for Switched Systems
Jun Zhao,David J. Hill +1 more
TL;DR: A frame work of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up, and asymptotic stability is guaranteed under certain "negative" output feedback.
References
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Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
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TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
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Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.