Switched nonlinear systems with state-dependent dwell-time

Persis, Claudio De; Santis, Raffaella De; Morse, A. Stephen

doi:10.1016/s0167-6911(03)00161-0

Cited by 138 publications

(33 citation statements)

References 15 publications

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“…A number of authors have further extended this work and derived analogous results for other classes of switched nonlinear systems [128,41]. Further developments have also included the work of Zhai et al [190] in which the authors modify this result so that the lowest average dwell-timeτ * D ensures that the switched system achieves a chosen L 2 gain, while several other authors have extended the results to allow for switching between stable and unstable subsystems, e.g.…”

Section: Constraints On the Rate Of Switchingmentioning

confidence: 92%

Stability Criteria for Switched and Hybrid Systems

Shorten¹,

Wirth²,

Mason³

et al. 2007

SIAM Rev.

900

558

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The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, and to review some problems that remain open. An important contribution of our work is to bring together material from several areas of research and to present results in a unified manner. We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent constructive methods for proving stability, and also represent problems in which significant progress has been made. We also comment on the inherent difficulty of determining stability of switched systems in general which is exemplified by NP-hardness and undecidability results. We then proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell time requirements and state dependent switching laws. Also in this case the theory of Lyapunov functions and the existence of converse theorems is reviewed. We briefly comment on the classical Lur'e problem and on the theory of stability radii, both of which contain many of the features of switched systems and are rich sources of practical results on the topic. Finally we present a list of questions and open problems which provide motivation for continued research in this area.

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Section: Constraints On the Rate Of Switchingmentioning

confidence: 92%

Stability Criteria for Switched and Hybrid Systems

Shorten¹,

Wirth²,

Mason³

et al. 2007

SIAM Rev.

900

558

View full text Add to dashboard Cite

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“…For more general matrices A,'s, similar conclusion can be drawn using arguments of the kind found in [IS] and [12]. o 5 …”

Section: Remarksupporting

confidence: 68%

“…Lemma 1 ( [3], [MI) For each p E P, there ezists a feedback law U = xp(x), such that the closed-loop system…”

Section: (13)mentioning

confidence: 99%

Further results on switched control of linear systems with constraints

Persis

Santis

Morse

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

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In a previous paper ([a], see also 131) we proposed a supervisory control system to globally regulate to zero the state of a very poorly modeled, open-loop unstable but not exponentially unstable, linear process in the p r e r ence of input constraints. The process to control was unknown but assumed to belong to a finite family P of nominal models. In this paper, the analysis is extended to the case in which P is not finite and is a closed, bounded subset of a real, finite-dimensional, normed linear space. In this analysis, the property of the multiestimator/multi-controller of being "robustly" integral input-to state stable is exploited.

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“…From well known results (Persis et al, 2003;Hespanha et al, 1999) about asymptotic stability of switched asymptotically stable systems for any switching law having a given dwell time, we need T window + t r < T active min (9) to guarantee uniform asymptotic stability of the closed-loop system for any switching signal having a minimum activation time T active min . Note that t r can be tuned using the α i and T window = κT s .…”

Section: Some Details About Control Designmentioning

confidence: 99%

“…More precisely on the stability and control issues, different operating tools have been proposed, such as multiple Lyapunov functions (Branicky, 1998), dwell-time (Persis et al, 2003) and average dwell time (Hespanha et al, 1999). Among all the problems linked to switched systems, two main questions are:…”

Section: Introductionmentioning

confidence: 99%