Discrete-time switched systems, set-theoretic analysis and quasi-quadratic Lyapunov functions

Author

Hetel, L. ; Kruszewski, A. ; Perruquetti, W. ; Richard, J.P.

Author_Institution

CNRS LAGIS, Ecole Centrale de Lille, Villeneuve-d´´Ascq, France

fYear

2011

fDate

20-23 June 2011

Firstpage

1325

Lastpage

1330

Abstract

The article establishes a constructive link between two approaches for analyzing the stability of discrete-time switched linear systems with arbitrary switching. The first approach is based on quasi-quadratic Lyapunov functions while the second one concerns a set-theoretic analysis of switched systems. An LMIs based procedure for deriving quasi-quadratic Lyapunov functions from the set-theoretic analysis is obtained. The approach may be used for constructing positively invariant sets for cases of switched discrete-time linear systems that are not quadratically stable.

Keywords

Lyapunov matrix equations; discrete time systems; linear matrix inequalities; linear systems; set theory; stability; LMI; discrete-time switched linear system stability; linear matrix inequalities; quasiquadratic Lyapunov function; set theoretic analysis; Linear systems; Lyapunov methods; Numerical stability; Stability analysis; Switches; Symmetric matrices; Tin; Linear Matrix Inequalities (LMIs); arbitrary switching; positively invariant sets; quasi-quadratic Lyapunov functions; stability; switched systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Control & Automation (MED), 2011 19th Mediterranean Conference on

Conference_Location

Corfu

Print_ISBN

978-1-4577-0124-5

Type

conf

DOI

10.1109/MED.2011.5983111

Filename

5983111