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Control Subject to Computational and Communication Constraints pp 25–46Cite as

Stabilizability and Control Co-Design for Discrete-Time Switched Linear Systems

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 475))

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 stabilizability 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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Authors and Affiliations

  1. University Grenoble Alpes, CNRS, Gipsa-lab, F-38000, Grenoble, France

    M. Fiacchini

  2. Université de Lorraine, CRAN, UMR 7039, 2 avenue de la forêt de Haye, Vandœuvre-lès-Nancy Cedex, 54516, Lorraine, France

    M. Jungers

  3. CNRS, CRAN, UMR 7039, Lorraine, France

    M. Jungers

  4. Laboratoire des signaux et systèmes (L2S), CNRS, CentraleSupélec, Université Paris-Sud, Université Paris-Saclay, 3, rue Joliot-Curie, 91192, Gif-sur-Yvette, cedex, France

    A. Girard

  5. LAAS-CNRS, Université de Toulouse, Toulouse, France

    S. Tarbouriech

Authors
  1. M. Fiacchini
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  2. M. Jungers
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  3. A. Girard
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  4. S. Tarbouriech
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Corresponding author

Correspondence to M. Fiacchini .

Editor information

Editors and Affiliations

  1. LAAS-CNRS, Université de Toulouse, Toulouse, France

    Sophie Tarbouriech

  2. Laboratoire des Signaux et Systèmes, CNRS, CentraleSupélec, Université Paris-Sud, Université Paris-Saclay, Gif-sur-Yvette, France

    Antoine Girard

  3. CNRS, Centrale Lille, UMR 9189—Centre de Recherche en Informatique Signal et Automatique de Lille (CRIStAL), Université Lille, Lille, France

    Laurentiu Hetel

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Fiacchini, M., Jungers, M., Girard, A., Tarbouriech, S. (2018). Stabilizability and Control Co-Design for Discrete-Time Switched Linear Systems. In: Tarbouriech, S., Girard, A., Hetel, L. (eds) Control Subject to Computational and Communication Constraints. Lecture Notes in Control and Information Sciences, vol 475. Springer, Cham. https://doi.org/10.1007/978-3-319-78449-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-78449-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78448-9

  • Online ISBN: 978-3-319-78449-6

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