Necessary and sufficient stability conditions for integral delay systems

TL;DR

This paper introduces a Lyapunov-Krasovskii functional approach to derive necessary and sufficient stability conditions for integral delay systems, using the delay Lyapunov matrix, with validation through examples.

Contribution

It presents a novel Lyapunov-Krasovskii functional that does not require system stability for construction, enabling explicit stability criteria based solely on the delay Lyapunov matrix.

Findings

Derived necessary and sufficient stability conditions

Functional evaluation depends on initial conditions and fundamental matrix

Validated conditions through illustrative examples

Abstract

A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at initial conditions depending on the fundamental matrix we are able to present necessary and sufficient stability conditions expressed exclusively in terms of the delay Lyapunov matrix for integral delay systems. Some examples illustrate and validate the stability conditions.