Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces

Authors:
Falk M. Hante;Mario Sigalotti
Affiliations:
hante@iecn.u-nancy.fr and mario.sigalotti@inria.fr;-
Venue:
SIAM Journal on Control and Optimization
Year:
2011

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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.