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Exponential stability of linear periodic difference-delay equations

Laurent Baratchart 1 Sébastien Fueyo 2 Jean-Baptiste Pomet 3, 4
2 CaGE - Control And GEometry
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper deals with stability of linear periodic time-varying difference delay systems, i.e. dynamical systems where a finite dimensional signal at a certain time is given as a linear time-varying function of its values at a finite number of delayed times. We give a necessary and sufficient condition for exponential stability, that is a generalisation of the one by Henry and Hale in the 1970s. It has a control theoretic interpretation in terms of the harmonic transfer function (HTF) of a corresponding linear control system.
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https://hal.inria.fr/hal-03500720
Contributor : Jean-Baptiste Pomet Connect in order to contact the contributor
Submitted on : Friday, January 28, 2022 - 12:07:02 PM
Last modification on : Sunday, May 1, 2022 - 3:17:48 AM

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papiergeneralisationhale.pdf
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  • HAL Id : hal-03500720, version 3
  • ARXIV : 2201.12066

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Laurent Baratchart, Sébastien Fueyo, Jean-Baptiste Pomet. Exponential stability of linear periodic difference-delay equations. 2022. ⟨hal-03500720v3⟩

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