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Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces

Falk Hante 1 Mario Sigalotti 1 
1 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
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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Submitted on : Tuesday, February 15, 2011 - 4:46:32 PM
Last modification on : Saturday, June 25, 2022 - 7:45:42 PM
Long-term archiving on: : Monday, May 16, 2011 - 3:17:41 AM

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Falk Hante, Mario Sigalotti. Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (2), pp.752-770. ⟨10.1137/100801561⟩. ⟨hal-00489958v3⟩

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