Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces

Falk Hante (1, 2) , Mario Sigalotti (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 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.

Domaines: Optimisation et contrôle [math.OC]

Falk Hante, Mario Sigalotti. Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces. 2010. ⟨hal-00489958v2⟩