English

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.

Keywords

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

R2 v1 2026-06-28T13:23:19.677Z