Exponential Stability for Hybrid Systems with Saturations

Mirko Fiacchini (1) , Sophie Tarbouriech (2) , Christophe Prieur (1)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

In this chapter, the problems of characterizing exponential stability and computing ellipsoidal estimations of the domain of attraction for saturated hybrid systems are addressed. Hybrid systems presenting saturations and nested saturations on the inputs involved in both the continuous-time and the discrete-time dynamics are considered. A class of set-valued maps, extensions of saturated functions, is determined, which provides geometrical characterization of exponential stability for hybrid nested saturated systems. Computation-oriented conditions for local and global exponential stability are given in the form of convex constraints.

Domaines: Systèmes dynamiques [math.DS]

Mirko Fiacchini, Sophie Tarbouriech, Christophe Prieur. Exponential Stability for Hybrid Systems with Saturations. Hybrid systems with constraints, ISTE Ltd and John Wiley & Sons Inc., pp.179-212, 2013, 978-1-84821-527-6. ⟨hal-00833678⟩