Stability of linear switched systems with quadratic bounds and Observability of bilinear 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 aim of this paper is to give sufficient conditions for a switched linear system defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function to be GUAS. We show that this property is equivalent to the uniform observability of a bilinear system defined on a subspace whose dimension is in most cases much smaller than the dimension of the switched system. Some sufficient conditions of uniform asymptotic stability are then deduced from the equivalence theorem, and illustrated by examples.

Mots clés: Switched systems; Asymptotic stability; Quadratic Lyapunov functions; Observability; Bilinear systems

Domaines: Optimisation et contrôle [math.OC]

Moussa Balde, Philippe Jouan. Stability of linear switched systems with quadratic bounds and Observability of bilinear systems. 2012. ⟨hal-00661224v1⟩