基于改进积分不等式的时变时滞系统稳定性分析  

Stability analysis of time-varying delay systems based on an improved integral inequalityinequalities

作　　者：李紫薇 姜偕富[1] 李敬莹 李佳峰 马雪乐 LI Ziwei;JIANG Xiefu;LI Jingying;LI Jiafeng;MA Xuele(School of Automation,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学自动化学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2024年第1期39-46,共8页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61174108)。

摘　　要：研究一类时变时滞线性系统的时滞相关稳定性问题。给出了一种改进的基于松弛矩阵的复合积分不等式(CSMBII)。它克服了Bessel-Legendre积分不等式中时滞变量h(t)出现在分母上的情况,使CSMBII能够更方便地处理时变时滞系统。在一定程度上克服了以往工作中的松弛矩阵与时变延迟无关的缺点。在CSMBII的基础上,运用Lyapunov稳定性理论,构造含有二重积分形式的Lyapunov-Krasovskii(L-K)泛函,导出了一种新的时滞相关稳定性判据。通过两个数值算例说明了稳定性判据的有效性。The delay-dependent stability problem of a class of linear systems with time-varying delay is studied.An improved Composite Slack-Matrix-Based Integral Inequality(CSMBII)is presented.It overcomes the restriction of mutual convexity in Bessel-Legendre integral inequalities and makes CSMBII more convenient to deal with time-varying delay systems.To some extent,it overcomes the disadvantage that relaxation matrix is independent of time-varying delay in previous work.On the basis of Based on CSMBII,a Lyapunov-Krasovskii(L-K)functional with double integral form is constructed by using Lyapunov stability theory,and a new delay-dependent stability criterion is derived.Two numerical examples are given to illustrate the validity of the stability criterion.

关 键 词：时变时滞系统 LYAPUNOV-KRASOVSKII泛函 复合松弛矩阵的积分不等式(CSMBII) 稳定性准则 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]