Robustness of stochastic discrete-time switched linear systems with application to control with shared resources

Luca Greco (1) , Antoine Chaillet (1) , Elena Panteley (1)

1 L2S - Laboratoire des signaux et systèmes

Motivated by control applications relying on shared resources (such as computation time or bandwidth), we analyze the stability and robustness of discrete-time switched linear systems driven by a stochastic process. The class of systems we study encompasses Markov Chain and independent and identically distributed switching processes. For these systems, we recall existing definitions of stability and robustness, by relying on the input-to-state (ISS) property. We show that, for the class of systems under concern, δ-moment stability is equivalent to its ISS counterpart and that they both imply almost sure ISS. Several sufficient conditions are provided to guarantee these properties. All the concepts are illustrated by the anytime control of a mechanical system.

Mots clés: Stochastic Jump Linear Systems; Input to state stability

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

Luca Greco, Antoine Chaillet, Elena Panteley. Robustness of stochastic discrete-time switched linear systems with application to control with shared resources. 2012. ⟨hal-00728093v1⟩