A characterization of switched linear control systems with finite L2-gain

Yacine Chitour (1, 2) , Paolo Mason (3, 2) , Mario Sigalotti (4, 5)

1 UP11 - Université Paris-Sud - Paris 11
2 L2S - Laboratoire des signaux et systèmes
3 CNRS - Centre National de la Recherche Scientifique
4 GECO - Geometric Control Design
5 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Motivated by an open problem posed by J.P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that finiteness of the L2-gain is equivalent, for a large set of switched linear control systems, to the condition that the generalized spectral radius associated with minimal realizations of the original switched system is smaller than one.

Domaines: Optimisation et contrôle [math.OC]

Yacine Chitour, Paolo Mason, Mario Sigalotti. A characterization of switched linear control systems with finite L2-gain. 2015. ⟨hal-01198394v1⟩