Stability criteria of linear delay differential systems based on fundamental matrix

TL;DR

This paper develops necessary and sufficient stability criteria for linear delay differential systems using integrals of the fundamental matrix, providing a comprehensive method for delay-dependent stability analysis.

Contribution

It introduces a novel stability criterion based on the fundamental matrix, enhancing the understanding of delay-dependent stability in linear systems.

Findings

Derived necessary and sufficient stability conditions

Provided numerical examples illustrating the criteria

Enhanced stability analysis methods for delay differential systems

Abstract

We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the systems. Numerical examples are given to illustrate the main results.