A Core Theory of Delay Systems

2017/07/09 by Sébastien Boisgérault, Boisgérault, Sébastien
Computer Science · Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1707.02558

openalex publication_date 2017/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a framework for the description of a large class of delay-differential algebraic systems, in which we study three core problems: first we characterize abstractly the well-posedness of the initial-value problem, then we design a practical test for well-posedness based on a graph-theoretic representation of the system; finally, we provide a general stability criterion. We apply each of these results to a structure that commonly arises in the control of delay systems.

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