Integral representation formula for linear non-autonomous difference-delay equations
Dynamical Systems
2024-10-07 v2
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.
Cite
@article{arxiv.2311.09842,
title = {Integral representation formula for linear non-autonomous difference-delay equations},
author = {Laurent Baratchart and Sébastien Fueyo and Jean-Baptiste Pomet},
journal= {arXiv preprint arXiv:2311.09842},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2201.12066