Exponential stability of linear periodic difference-delay equations

2022/01/28 by Laurent Baratchart, Baratchart, Laurent, Sébastien Fueyo +3
Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2201.12066

openalex publication_date 2022/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the stability of linear periodic difference delay systems, where the value at time t of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants t-τ₁,…,t-τ_N. We establish a necessary and sufficient condition for exponential stability of such systems when the coefficients have Hölder-continuous derivative, that generalizes the one obtained for difference delay systems with constant coefficients by Henry and Hale in the 1970s. This condition may be construed as analyticity, in a half plane, of the (operator valued) harmonic transfer function of an associated linear control system.

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