基于二重Wirtinger型积分不等式变时滞系统稳定性判据

Stability Criterion of Time-Varying Delay Systems via Wirtinger-Based Double Integral Inequality

为解决带有时变时滞线性系统的稳定性问题,本文以李雅普诺夫稳定性理论为基础,构造了增广型的李雅普诺夫泛函,在推导技术上推广了文献[1]的二重Wirtinger型积分不等式,给出了新的区间时变时滞系统稳定性判别方法,为说明本文结果的优越性,应用数值例子进行验证。验证结果表明,本文可以获得更大的时滞上限,所提出的方法更加优越,说明了本文结果具有更低的保守性。本研究对中立型等时滞系统的稳定性判定具有较好的应用价值。

This paper is concerned with the problem of the stability of the time-varying delay systems. Based on Lyapunov stability theory, an appropriate Lyapunov-Krasovskii functional is proposed and a new stability criterion for the time varying delay systems is obtained in terms of linear matrix inequalities. The main techniques used include the reciprocally convex method and the extended inequalities based on the wirtinger-based double integral inequality. The results are shown less conservative than the existing ones by using numerical examples. The result of the study also can be applied to neutral delay systems.