Time-Transformation-Based Analysis of Systems with Periodic Delay via Perturbative Expansion
Abstract
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the system matrices. The stability of this transformed system can then be analyzed using methods to bound the effect of the time-varying scalar. One issue is that this transformation is non-unique and requires the solution of an Abel equation. A specific time-transformation typically must be computed numerically. We address this issue by computing an explicit, although approximate, time-transformation for systems where the delay has a constant plus small periodic term. We use a perturbative expansion to construct our explicit solutions. We provide a simple numerical example to illustrate the approach. We also demonstrate the use of this time-transformation to analyze stability of the system with this class of periodic delays.
Cite
@article{arxiv.2603.15961,
title = {Time-Transformation-Based Analysis of Systems with Periodic Delay via Perturbative Expansion},
author = {Jungbae Chun and Sengiyumva Kisole and Matthew M. Peet and Peter Seiler},
journal= {arXiv preprint arXiv:2603.15961},
year = {2026}
}