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On the Stability Analysis of Sampled-Data Systems with Delays

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Delays and Networked Control Systems

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

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Abstract

Controlling a system through a network amounts to solve certain difficulties such as, among others, the consideration of aperiodic sampling schemes and (time-varying) delays. In most of the existing works, delays have been involved in the input channel through which the system is controlled, thereby delaying in a continuous way the control input computed by the controller. We consider here a different setup where the delay acts in a way that the current control input depends on past state samples, possibly including the current one, which is equivalent to considering a discrete-time delay, at the sample level, in the feedback loop. An approach based on the combination of a discrete-time Lyapunov–Krasovskii functional and a looped-functional is proposed and used to obtain tailored stability conditions that explicitly consider the presence of delays and the aperiodic nature of the sampling events. The stability conditions are expressed in terms of linear matrix inequalities and the efficiency of the approach is illustrated on an academic example.

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Authors and Affiliations

  1. LAAS-CNRS, Université de Toulouse, CNRS, 7 avenue du Colonel Roche, 31077, Toulouse, France

    Alexandre Seuret

  2. Department of Biosystems Science and Engineering (D-BSSE), Swiss Federal Institute of Technology Zurich (ETH-Z), Mattenstrasse 26, 4058, Basel, Switzerland

    Corentin Briat

Authors
  1. Alexandre Seuret
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  2. Corentin Briat
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Correspondence to Alexandre Seuret .

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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Seuret, A., Briat, C. (2016). On the Stability Analysis of Sampled-Data Systems with Delays. 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_6

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  • DOI: https://doi.org/10.1007/978-3-319-32372-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32371-8

  • Online ISBN: 978-3-319-32372-5

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