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

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.

Mots clés: Switched systems; Strongly continuous semigroups; Lyapunov function; Exponential stability

Domaines: Optimisation et contrôle [math.OC]

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