A Core Theory of Delay Systems

TL;DR

This paper develops a comprehensive framework for analyzing delay-differential algebraic systems, including well-posedness, a graph-based test, and stability criteria, with applications in control systems.

Contribution

It introduces a unified approach to characterize well-posedness, design practical tests, and establish stability conditions for delay systems, advancing theoretical understanding.

Findings

A graph-theoretic test for well-posedness

A general stability criterion for delay systems

Application to control-related delay structures

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.