Stability Analysis of Integral Delay Systems with Multiple Delays

TL;DR

This paper develops new less conservative stability criteria for integral delay systems with multiple delays using generalized Jensen inequalities and Lyapunov functionals, improving upon existing methods.

Contribution

It introduces novel Lyapunov functional approaches with optimized Jensen inequalities for less conservative stability analysis of multi-delay systems.

Findings

New stability conditions expressed as LMIs are less conservative.

A spectral radius based stability condition is proposed.

Numerical example confirms the effectiveness of the methods.

Abstract

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.