Multiple integral inequalities and stability analysis of time delay systems

TL;DR

This paper introduces new multiple integral inequalities for stability analysis of continuous-time delay systems, unifying existing inequalities and establishing a hierarchy of LMIs to compare their conservatism.

Contribution

It develops a set of novel multiple integral inequalities and a hierarchical LMI framework for more accurate stability analysis of delay systems.

Findings

The proposed inequalities improve stability condition accuracy.

A hierarchy of LMIs allows comparison of different methods.

Numerical examples demonstrate the method's efficiency.

Abstract

This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen's and Wirtinger's inequalities, as well as the recently presented Bessel-Legendre inequalities of A. Seuret and F. Gouaisbaut, (2015) and the Wirtinger-based multiple-integral inequalities of M. Park et al. (2015) and T.H. Lee et al. (2015). The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.