Stabilization and control Lyapunov functions for language constrained discrete-time switched linear systems

Mirko Fiacchini (1) , Marc Jungers (2) , Antoine Girard (3)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 CRAN - Centre de Recherche en Automatique de Nancy
3 L2S - Laboratoire des signaux et systèmes

In this paper, the stabilizability of discrete-time switched linear systems subject to constraints on the switching law is considered. The admissible switching sequences are given by the language generated by a nondeterministic finite state automaton. Constructive necessary and sufficient conditions for recurrent stabilizability are given and the exact relations with the existence of control Lyapunov functions and with general stabilizability are provided. The dependence of stabilizability on the automaton initial state is also proved.

Mots clés: set-theory; Switched linear systems; automata; stabilizability

Domaines: Automatique / Robotique; Systèmes dynamiques [math.DS]

Mirko Fiacchini, Marc Jungers, Antoine Girard. Stabilization and control Lyapunov functions for language constrained discrete-time switched linear systems. Automatica, 2018, 93, pp.64-74. ⟨10.1016/j.automatica.2018.03.039⟩. ⟨hal-01677493⟩