Constructive necessary and sufficient condition for the stability of quasi-periodic linear impulsive systems

Mirko Fiacchini (1) , Irinel-Constantin Morarescu (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 CRAN - Centre de Recherche en Automatique de Nancy

The paper provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, the existence of polyhedral Lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi-periodic linear impulsive systems. A constructive method is developed for testing the stability of the system and for computing set-induced polyhedral Lyapunov functions. The method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete-time parametric uncertain systems with the state matrix belonging to a convex polytopic set.

Mots clés: Reset systems; stability analysis; set theory

Domaines: Automatique

Mirko Fiacchini, Irinel-Constantin Morarescu. Constructive necessary and sufficient condition for the stability of quasi-periodic linear impulsive systems. IEEE Transactions on Automatic Control, 2016, 61 (9), pp.2512-2517. ⟨10.1109/TAC.2015.2496792⟩. ⟨hal-01379018⟩