Geometry of the Limit Sets of Linear Switched Systems

Moussa Balde (1) , Philippe Jouan (2)

1 Département de Mathématiques et Informatique, Faculté des Sciences et Techniques
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions of inputs with dwell time. Next we turn our attention to the behaviour for possibly chaotic inputs. To finish we give a sufficient condition for a system composed of a pair of Hurwitz matrices to be asymptotically stable for all inputs.

Mots clés: Switched systems; Asymptotic stability; Quadratic Lyapunov functions; Chaotic signals; Omega-limit sets

Domaines: Optimisation et contrôle [math.OC]

Moussa Balde, Philippe Jouan. Geometry of the Limit Sets of Linear Switched Systems. SIAM Journal on Control and Optimization, 2011, 49 (3), pp.1048-1063. ⟨hal-00475844⟩