Stabilizability and control co-design for discrete-time switched linear systems

Mirko Fiacchini 1 Marc Jungers 2 Antoine Girard 3 Sophie Tarbouriech 4
1 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
2 CRAN - Centre de Recherche en Automatique de Nancy
3 L2S - Laboratoire des signaux et systèmes
4 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : In this work we deal with the stabilizability property for discrete-time switched linear systems. First we provide a constructive necessary and sufficient condition for stabilizability based on set-theory and the characterization of a universal class of Lyapunov functions. Such a geometric condition 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 convexity. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabiliz-ability conditions are analyzed to infer and compare their conservatism and their complexity. The results are finally extended to the problem of the co-design of a control policy, composed by both the state feedback and the switching control law, for discrete-time switched linear systems. Constructive conditions are given in form of LMI that are necessary and sufficient for the stabilizability of systems which are periodic stabilizable.
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LAAS | CRAN | TDS-MACS | LAAS-MAC | CENTRALESUPELEC | INSA-TOULOUSE | UNIV-LORRAINE | SUP_LSS | L2S | LAAS-DECISION-ET-OPTIMISATION | UGA | UNIV-PARIS-SACLAY | SUP_SYSTEMES | GIPSA | GIPSA-DA | GIPSA-SYSCO | INSA-GROUPE | UNIV-TLSE3

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Mirko Fiacchini, Marc Jungers, Antoine Girard, Sophie Tarbouriech. Stabilizability and control co-design for discrete-time switched linear systems. Tarbouriech, Sophie and Girard, Antoine and Hetel, Laurentiu. Control Subject to Computational and Communication Constraints, 475, Springer, pp.25-46, 2018, Lecture Notes in Control and Information Sciences, 978-3-319-78448-9. ⟨10.1007/978-3-319-78449-6_2⟩. ⟨hal-01856317⟩

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