A Nonlinear Small-Gain Theorem for Large-Scale Time Delay Systems

TL;DR

This paper extends the nonlinear ISS small-gain theorem to large-scale systems with time delays, providing a new theoretical framework applicable to a broad class of delayed differential systems.

Contribution

It introduces a small-gain theorem for operators that enables the analysis of large-scale time delay systems, expanding existing nonlinear stability results.

Findings

The theorem applies to systems with multiple delays.

It broadens the scope of small-gain theorems to operator-based systems.

The results facilitate stability analysis of complex delayed systems.

Abstract

This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.