Stability and stabilizability of discrete-time dual switching systems with application to sampled-data systems

Lucien Etienne (1) , Antoine Girard (2) , Luca Greco (2)

1 IMT Lille Douai - Ecole nationale supérieure Mines-Télécom Lille Douai
2 L2S - Laboratoire des signaux et systèmes

In this paper, stability and stabilizability of discrete-time dual switching linear systems is investigated. The switched systems under consideration have two switching variables. One of them is stochastic, described by an underlying Markov chain; the other one can be regarded either as a deterministic disturbance or as a control input, leading to stability or stabilizability problems, respectively. For the considered class of systems, sufficient conditions for mean square stability (with or without control gain synthesis) and mean square stabilizability are provided in terms of matrix inequalities. When the stochastic switching is driven by an independent identically distributed sequence, we establish simpler conditions without additional conservatism. Then, it is shown how the proposed framework can be used to study aperiodic sampled-data systems with stochastic computation times. The results are illustrated on examples borrowed from the literature.

Mots clés: Switched systems; Markov jump linear systems; Matrix inequalities; Sampled-data systems; Scheduling

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique; Systèmes et contrôle [cs.SY]

Lucien Etienne, Antoine Girard, Luca Greco. Stability and stabilizability of discrete-time dual switching systems with application to sampled-data systems. Automatica, 2019, 100, pp.388-395. ⟨10.1016/j.automatica.2018.11.014⟩. ⟨hal-02286513⟩