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Improved Synthesis of Saturating Sampled-Data Control Laws for Linear Plants

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Hybrid and Networked Dynamical Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 493))

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Abstract

The focus of this chapter is the stabilization of linear systems under saturating aperiodic sampled-data control. By employing a hybrid system representation, we establish conditions for the local and global stability of the origin of the closed-loop system using a specific class of quadratic timer (clock) dependent Lyapunov functions. These conditions are formulated as Sum-of-Squares constraints within optimization problems, enabling the design of stabilizing control laws that aim to maximize an estimate of the Region of Attraction to the Origin (RAO) or to maximize the admissible interval between two sampling instants in order to ensure that a certain given set of initial conditions is included in the RAO.

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Notes

  1. 1.

    The level set \(\mathcal{E}_{P}^{x_p}\) corresponds to (9.9) in the case where \(V(\eta )=x'P(\tau )x\) and, since P can be normalized, \(\mu \) can be considered as 1 without loss of generality in this case.

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Acknowledgements

This work was supported in part by the “Agence Nationale de la Recherche” (ANR, France) under Grant HANDY ANR-18-CE40-0010, by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Brazil)-Finance Code 001, and by the Conselho Nacional de Desenvolvimento Cientfico e Tecnológico (CNPq, Brazil) - under Grant PQ-307449/2019-0.

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Authors and Affiliations

  1. Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brazil

    Arthur Scolari Fagundes & João Manoel Gomes da Silva Jr.

  2. Université de Lorraine, CNRS, CRAN, 54000, Nancy, France

    Marc Jungers

Authors
  1. Arthur Scolari Fagundes
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  2. João Manoel Gomes da Silva Jr.
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  3. Marc Jungers
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Corresponding author

Correspondence to João Manoel Gomes da Silva Jr. .

Editor information

Editors and Affiliations

  1. Department Contrôle Identification Diagnostic, CNRS, Université de Lorraine, CRAN, Vandoeuvre-lès-Nancy, France

    Romain Postoyan

  2. DANCE INRIA, Gipsa-lab, CNRS, Saint Martin d’Hères, Isère, France

    Paolo Frasca

  3. MODESTY, L2S CNRS, CentraleSupélec, Gif-sur-Yvette, France

    Elena Panteley

  4. MAC, LAAS-CNRS, Toulouse, France

    Luca Zaccarian

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Fagundes, A.S., Gomes da Silva Jr., J.M., Jungers, M. (2024). Improved Synthesis of Saturating Sampled-Data Control Laws for Linear Plants. In: Postoyan, R., Frasca, P., Panteley, E., Zaccarian, L. (eds) Hybrid and Networked Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 493. Springer, Cham. https://doi.org/10.1007/978-3-031-49555-7_9

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  • DOI: https://doi.org/10.1007/978-3-031-49555-7_9

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  • Print ISBN: 978-3-031-49554-0

  • Online ISBN: 978-3-031-49555-7

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