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Preprints, Working Papers, ... Year : 2023

Exponential stability of linear periodic difference-delay equations

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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Dates and versions

hal-03500720 , version 1 (22-12-2021)
hal-03500720 , version 2 (22-12-2021)
hal-03500720 , version 3 (28-01-2022)
hal-03500720 , version 4 (17-07-2022)
hal-03500720 , version 5 (13-11-2023)

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Laurent Baratchart, Sébastien Fueyo, Jean-Baptiste Pomet. Exponential stability of linear periodic difference-delay equations. 2023. ⟨hal-03500720v5⟩
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