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arXiv · 2311.09842

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

Laurent Baratchart·Sébastien Fueyo·Jean-Baptiste Pomet
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Abstract

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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Laurent Baratchart, Sébastien Fueyo, Jean-Baptiste Pomet. 2023-11-16. Integral representation formula for linear non-autonomous difference-delay equations. https://doi.org/10.1216/jie.2024.36.407

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