A Numerical Technique for Stability Analysis of Linear Switched Systems

Yfoulis, Christos; Shorten, Robert

doi:10.1007/978-3-540-24743-2_42

Cited by 23 publications

(37 citation statements)

References 34 publications

(91 reference statements)

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“…This problem is partially avoided in the ray-gridding method developed by Yfoulis and his co-authors in [184,186,187]. The approach is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity.…”

Section: Common Piecewise Linear Lyapunov Functionsmentioning

confidence: 99%

Stability Criteria for Switched and Hybrid Systems

Shorten¹,

Wirth²,

Mason³

et al. 2007

SIAM Rev.

Self Cite

887

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: Common Piecewise Linear Lyapunov Functionsmentioning

confidence: 99%

Stability Criteria for Switched and Hybrid Systems

Shorten¹,

Wirth²,

Mason³

et al. 2007

SIAM Rev.

Self Cite

887

558

View full text Add to dashboard Cite

show abstract

“…A linear programming based method for solving these conditions was given by Polański in [28]. Recently, in [40], Yfoulis and Shorten proposed a numerical approach, called ray-griding, to calculate polyhedral Lyapunov functions based on uniform partitions of the state-space in terms of ray directions.…”

Section: A Polytopic Lyapunov Functionsmentioning

confidence: 99%

Switching Stabilizability for Continuous-Time Uncertain Switched Linear Systems

Lin

Antsaklis

2007

IEEE Trans. Automat. Contr.

146

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Abstract-This paper investigates the switching stabilizability problem for a class of continuous-time switched linear systems with time-variant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived, under the assumption that the closed-loop switched system does not generate sliding motions. Then, an additional condition is introduced to exclude the possibility of unstable sliding motions. Finally, a necessary and sufficient for the asymptotic stabilizability of such continuous-time uncertain switched linear systems is presented. This result improves upon conditions found in the literature which are either sufficient only or necessary only.

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“…To this end, flexible piecewise linear (PL) Lyapunov functions proposed recently in [17] are utilized, which rely on ray-gridding as a systematic technique for dealing with low dimensional PL systems via the construction of UDOAs using PL Lyapunov functions. The technique has been applied successfully to several different linear switched system analysis and design problems in the past [21,22,23].…”

Section: Control Design Through Bifurcation Analysis and Constrained mentioning

confidence: 99%

“…The two curves do not intersect, since there are always two different solutions k 21,22 . All these suggest, that for a-priori known bounds for the varying parameters V in , R we are able to specify precisely the bifurcation boundary between one and three real equilibria.…”

Section: Proof Of Lemmamentioning

confidence: 99%

Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

Yfoulis

Giaouris

Stergiopoulos

et al. 2015

Control Engineering Practice

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This paper proposes a new methodology for designing robust affine state-feedback control laws, so that wide-range safe and efficient operation of switched-mode DC-DC boost converters is guaranteed. Several undesirable nonlinear phenomena such as unstable attractors and subharmonic oscillations are avoided through bifurcation analysis based on the bilinear averaged model of the converter. The control design procedure also relies on constrained stabilization principles and the generation of safety domains using piecewise linear Lyapunov functions, so that robustness to supply voltage and output load variations is ensured, while input saturation is avoided and additional state constraints are also respected. The technique has been numerically and experimentally validated.

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A Numerical Technique for Stability Analysis of Linear Switched Systems

Cited by 23 publications

References 34 publications

Stability Criteria for Switched and Hybrid Systems

Stability Criteria for Switched and Hybrid Systems

Switching Stabilizability for Continuous-Time Uncertain Switched Linear Systems

Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

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