Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces

Abstract. We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes.

• Type: Journal
• Year: 2011
• Where: SIAMCO
• Authors: Falk M. Hante, Mario Sigalotti
• Keywords: Global Exponential Stability, Linear Evolution Operators, Lyapunov Function, SIAMCO 2011, Software Engineering