Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces (1006.1749v3)

Published 9 Jun 2010 in math.OC and cs.SY

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.

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