Finite Necessary and Sufficient Stability Conditions for Linear System with Pointwise and Distributed Delays

TL;DR

This paper introduces necessary and sufficient exponential stability conditions for linear systems with multiple pointwise and distributed delays, using delay Lyapunov and fundamental matrices, with a finite computational process.

Contribution

It provides the first finite-operation stability criteria for such delayed systems based on delay Lyapunov and fundamental matrices.

Findings

Stability criteria are necessary and sufficient.

Conditions are expressed via delay Lyapunov and fundamental matrices.

The stability test requires only a finite number of operations.

Abstract

This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the fundamental matrix of the system. An important property is that the stability test requires a finite number of mathematical operations.