Language constrained stabilization of discrete-time switched linear systems: an LMI approach

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

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

The goal of this paper is to study sufficient conditions to stabilize an autonomous discrete-time switched system, for which the switching law should belong to a constrained language characterized by a nondeterministic automaton. Based on a decomposition into strongly connected components of the automaton, it is shown that it suffices to consider only a nontrivial strongly connected component. Sufficient conditions are provided as a set of Linear Matrix Inequalities (LMIs) related to the automaton states and associated with a min-switching strategy. Equivalence with the periodic stabilization is investigated. A numerical example is provided to illustrate the main result.

Mots clés: Switched systems; Stabilizability; LMI; Automaton; Language constrained

Domaines: Automatique / Robotique

Marc Jungers, Antoine Girard, Mirko Fiacchini. Language constrained stabilization of discrete-time switched linear systems: an LMI approach. 6th IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2018, Jul 2018, Oxford, United Kingdom. ⟨10.1016/j.ifacol.2018.08.005⟩. ⟨hal-01899003⟩