基于Wirtinger积分不等式变时滞广义系统稳定性分析  

Stability Analysis of Singular Systems with Time-Varying Delays via Wirtinger-Based Integral Inequality

作　　者：杨志宏[1] 林崇[1] 马瑞兰[1] 

机构地区：[1]青岛大学复杂性科学研究所,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2017年第3期8-14,共7页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金资助项目(61673227)

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。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.

关 键 词：变时滞广义系统 稳定性 线形矩阵不等式 二重Wirtinger型积分不等式 

分 类 号：O175[理学—数学]