CONVERSE LYAPUNOV THEOREMS FOR SWITCHED SYSTEMS IN BANACH AND HILBERT SPACES

摘要

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.