A Converse Lyapunov Theorem for Uncertain Switched Linear Systems

Hai Lin and Panos J. Antsaklis

Proceedings of the 44th Conference on Decision and Control
Seville, Spain, December 12-15, 2005

Abstract—The main contribution of this paper is a converse Lyapunov theorem derived for a class of switched linear systems with time-variant parametric uncertainties. Both discrete-time and continuous-time switched linear systems are investigated. It is shown that the existence of asymptotically stabilizing switching laws implies the existence of a polyhedral Lyapunov function along with conic partition based stabilizing switching laws. The results presented here could be an important step towards a necessary and sufficient condition for stabilizability of switched linear systems. The methods here are based on real analysis and polyhedral algebra.

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