Necessary and sufficient condition for stabilizability of discrete-time linear switched systems: A set-theory approach (original) (raw)
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This paper is concerned with the robust stability and stabilization for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability and stabilization of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability and stabilization have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method, and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.
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During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.
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2005
During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.
Stabilization of Continuous-time and Discrete-time Switched Systems : A Review *
2017
Stability problem for a class of linear continuous time and discrete time systems is well understood since long. This analysis has also been extended to switched linear systems with continuous and discrete descriptions. For such cases, arbitrary switching problem is addressed by constructing common quadratic and non-quadratic Lyapunov function. Moreover, keeping in view the invertible time delays in dynamical systems due to internal factors or external environment, study of switched systems with delays has become quite challenging. The present work, highlights the state of art review of switched systems and underlying methodologies to ensure stabilization of such system with individual systems having stable or unstable dynamics. Further, current status and future directions of possible scope and open challenges in this area are also highlighted for completeness.
Static switched output feedback stabilization for linear discrete-time switched systems
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IFAC-PapersOnLine, 2020
This paper addresses Lyapunov characterizations of input-to-state stability for nonlinear switched discrete-time systems via finite-step Lyapunov functions with respect to closed sets. The use of finite-step Lyapunov functions permits not-necessarily input-to-state stable systems in the systems family, while input-to-state stability of the resulting switched system is ensured. The result is generally presented for systems under arbitrary switching. It additionally covers the case of constrained switchings. We illustrate the effectiveness of our results by application to networked control systems with periodic scheduling policies under a priori known and dwell time-based switching mechanism.
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2007
In this paper, the problem of finding a stabilizing feedback controller for single input single output switched systems of order two is addressed. To ensure stability under arbitrary switching, the existence of a common Lyapunov function (CLF) needs to be established. A method for establishing the existence of CLFs, given suitable feedback controllers, is presented. The method presented here is computationally less demanding compared to those that depend on linear matrix inequalities solvers.