不等式的推广以及在加性时变时滞系统中的应用  

Generalization of Inequality and Its Application in Additive Time-Varying Delay Systems

作　　者：樊天娇 冯立超 杨艳梅 Fan Tianjiao;Feng Lichao;Yang Yanmei(College of Sciences,North China University of Science and Technology,Hebei Tangshan 063210)

机构地区：[1]华北理工大学理学院,河北唐山063210

出　　处：《数学物理学报（A辑）》2024年第5期1335-1351,共17页Acta Mathematica Scientia

基　　金：教育部人文社会科学研究规划基金(23YJAZH031);河北省自然科学基金(A2023209002,A2019209005);唐山市科学技术研究与发展计划项目(19130222g)。

摘　　要：该文主要研究积分不等式的改进问题,并将其应用于加性时变时滞系统的稳定性研究:首先,采用含参函数构造方法,从单调性和增加正项两个角度,对现有的Wirtinger不等式进行了证明;其次,提出了扩展不等式,其中包括扩展Wirtinger不等式和基于三阶矩阵的扩展互凸不等式;再次,分别利用这两个扩展不等式,以线性矩阵不等式的形式给出了加性时变时滞系统渐近稳定的判定准则;最后,通过数值算例说明所提方法的优越性.This article mainly studies the improvement problem of integral inequality and applies it to the stability study of additive time-varying delay systems:Firstly,the existing Wirtinger inequal-ity is proven from the perspectives of monotonicity and adding positive terms using the method of constructing parameter functions.Secondly,we propose extended inequalities,including the extended Wirtinger inequality and the extended cross-convex inequality which is based on third-order matrices.Thirdly,utilizing these two extended inequalities,we provide criteria for determining the asymptotic stability of additive time-varying delay systems in the form of Linear Matrix Inequalities(LMIs).Final-ly,numerical examples are presented to demonstrate the effectiveness and superiority of the proposed method.

关 键 词：加性时变时滞系统 WIRTINGER不等式 稳定性分析 

分 类 号：O211[理学—概率论与数理统计]