Exponential stability of time-delay systems via new weighted integral inequalities

TL;DR

This paper introduces new weighted integral inequalities that improve stability analysis of time-delay systems, reducing conservativeness and unifying previous inequalities, with demonstrated effectiveness through numerical examples.

Contribution

The paper derives novel weighted integral inequalities that generalize and improve existing inequalities, enhancing exponential stability analysis of time-delay systems within the LMI framework.

Findings

New WIIs encompass Jensen and Wirtinger inequalities.

Stability conditions using WIIs are less conservative.

Numerical examples confirm improved stability analysis.

Abstract

In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvements based on Wirtinger integral inequality. The potential capability of the proposed WIIs is demonstrated through applications in exponential stability analysis for some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.