Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces

Details Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces

2010-06-09

arxiv.org/abs/1006.1749v3

Mathematics

Optimization and Control

Scientific paper

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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