A Necessary and Sufficient Condition for Robust Asymptotic Stabilizability of Continuous-Time Uncertain Switched Linear Systems

Hai Lin and Panos J.Antsaklis

Proceedings of the 43rd Conference on Decision and Control , pp. 3690-3695, Paradise Island, The Bahamas, December 14-17, 2004.

Abstract—The main contribution of this paper is a necessary and sufficient condition derived for the existence of asymptotically stabilizing switching laws for a class of switched linear systems with time-variant parametric uncertainties. This result improves upon the sufficient only conditions found in the literature. The method is based on polyhedral Lyapunovlike functions, which represent generalizations of polytopic Lyapunov functions in the classical sense.

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