On the stabilizability of discrete-time switched linear systems: novel conditions and comparisons

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

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

In this paper we deal with the stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity.

Mots clés: Switched systems; stabilizability; LMI

Domaines: Automatique / Robotique

Mirko Fiacchini, Antoine Girard, Marc Jungers. On the stabilizability of discrete-time switched linear systems: novel conditions and comparisons. IEEE Transactions on Automatic Control, 2016, 61 (5), pp.1181-1193. ⟨10.1109/TAC.2015.2450871⟩. ⟨hal-01185649v2⟩