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Pré-Publication, Document De Travail Année : 2023

Integral representation formula for linear non-autonomous difference-delay equations

Résumé

This note states and proves an integral representation formula of the "variation-of-constant" type for continuous solutions of linear non-autonomous difference delay systems, in terms of a Lebesgue-Stieltjes integral involving a fundamental solution and the initial data of the system. This gives a precise and correct version of several formulations appearing in the literature, and extends them to the time-varying case. This is of importance for further stability studies of various kinds of delay systems.
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Dates et versions

hal-04204500 , version 1 (12-09-2023)
hal-04204500 , version 2 (16-11-2023)
hal-04204500 , version 3 (05-06-2024)

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Laurent Baratchart, Sébastien Fueyo, Jean-Baptiste Pomet. Integral representation formula for linear non-autonomous difference-delay equations. 2023. ⟨hal-04204500v3⟩
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