中文摘要：

针对线性变时滞广义系统的稳定性问题,本文以Lyapunov稳定性理论作为理论基础,在推导技术上通过构造增广的Lyapunov-Krasovskii泛函,结合推广的二重Wirtinger型积分不等式,并利用一阶和二阶倒数凸组合的方法,获得了新的基于二重Wirtinger型积分不等式线性时变时滞广义系统时滞相关的稳定性判据,并通过Matlab中的线性矩阵不等式工具箱求解,应用数值例子进行验证。验证结果表明,与文献[20]相比,定理1方法可以获得更大的时滞允许上限,说明本文的结果具有更低的保守性。该理论成果对于研究变时滞系统稳定性分析方法有重要意义。

英文摘要：

This paper is concerned with the problem of the stability analysis of the linear singular systems with time-varying delays. Based on Lyapunov stability theory,an appropriate Lyapunov-Krasovskii functional is con-structed. By using Wirtinger-based double integral inequality method and reciprocally convex method, a suffi-cient stability criterion is obtained. The conditions are in terms of linear matrix inequalities （LMIs）. Then, a numerical example is given for illustration. The results are shown less conservative than the existing ones. The present method is of great significance for stability analysis of time-varying delay systems.