Stability of uniformly bounded switched systems and Observability

Moussa Balde (1) , Philippe Jouan (2) , Said Naciri (2)

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

This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS. We show that this property of being GUAS is equivalent to the uniform observability on $[0,+\infty)$ 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. The results are partially extended to nonlinear analytic systems.

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

Domaines: Optimisation et contrôle [math.OC]

Moussa Balde, Philippe Jouan, Said Naciri. Stability of uniformly bounded switched systems and Observability. Acta Applicandae Mathematicae, 2016, ⟨10.1007/s10440-015-0039-9⟩. ⟨hal-00661224v2⟩