Lyapunov Functions for Shuffle Asymptotic Stability of Discrete-Time Switched Systems

Antoine Girard (1) , Paolo Mason (1)

1 L2S - Laboratoire des signaux et systèmes

In this paper, we investigate stability of discrete-time switched systems under shuffled switching signals. A switching signal is said to be shuffled if each mode of the switched system is activated infinitely often. We introduce the notion of shuffle Lyapunov functions and show that the existence of such a function is a sufficient condition for global uniform shuffle asymptotic stability. In the second part of the paper, we show that for a specific class of switched systems, with linear and invertible dynamics, existence of a shuffle Lyapunov function is also necessary, even for the weaker notion of global shuffle attractivity. Examples and numerical experiments are used to illustrate the main results of the paper.

Mots clés: Switched systems; Shuffle stability; Lyapunov methods

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique; Systèmes et contrôle [cs.SY]

Antoine Girard, Paolo Mason. Lyapunov Functions for Shuffle Asymptotic Stability of Discrete-Time Switched Systems. IEEE Control Systems Letters, 2019, 3 (3), pp.499-504. ⟨10.1109/LCSYS.2019.2909731⟩. ⟨hal-02286590⟩