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Stability and Stabilization for Continuous-Time Difference Equations with Distributed Delay

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Delays and Networked Control Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 6))

Abstract

Motivated by linear hyperbolic conservation laws , we investigate in this chapter new conditions for stability and stabilization for linear continuous-time difference equations with distributed delay . For this, we propose first a state-space realization of networks of linear hyperbolic conservation laws via continuous-time difference equations. Then, based on some recent works, we propose sufficient conditions for exponential stability , which appear also to be necessary and sufficient in some particular cases. Then, the stabilization problem as well as the closed-loop performances are analyzed with constructive methods for state feedback synthesis.

This chapter represents an extended version of the conference proceedings paper [14].

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Authors and Affiliations

  1. Université de Lyon, Laboratoire Ampère, UMR CNRS 5005, INSA-Lyon, 20 Avenue Albert Einstein, 69621, Villeurbanne, France

    Michael Di Loreto & Sérine Damak

  2. Departamento de Control Automatico, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, 07360, Del. G.A. Madero, Mexico D.F., Mexico

    Sabine Mondié

Authors
  1. Michael Di Loreto
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  2. Sérine Damak
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  3. Sabine Mondié
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Correspondence to Michael Di Loreto .

Editor information

Editors and Affiliations

  1. LAAS—UPR CNRS, Université de Toulouse, Toulouse, France

    Alexandre Seuret

  2. CRISTAL—UMR CNRS, École centrale de Lille, Villeneuve d'Ascq Cedex, France

    Laurentiu Hetel

  3. Université de Lorraine, CRAN—UMR CNRS, INPL,, Vandoeuvre-lès-Nancy Cedex, France

    Jamal Daafouz

  4. School of Electrical Engineering, Royal Institute of Technology, Stockholm, Sweden

    Karl H. Johansson

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Di Loreto, M., Damak, S., Mondié, S. (2016). Stability and Stabilization for Continuous-Time Difference Equations with Distributed Delay. In: Seuret, A., Hetel, L., Daafouz, J., Johansson, K. (eds) Delays and Networked Control Systems . Advances in Delays and Dynamics, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-32372-5_2

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  • DOI: https://doi.org/10.1007/978-3-319-32372-5_2

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