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
李紫薇 1姜偕富 1李敬莹 1李佳峰 1马雪乐1
作者信息
- 1. 杭州电子科技大学自动化学院,浙江杭州 310018
- 折叠
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.
Abstract
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Key words
Time-varying delay system/Lyapunov-Krasovskii functional/Composite slack-matrix-based integral inequality(CSMBII)/Stability criterion引用本文复制引用
基金项目
国家自然科学基金资助项目(61174108)
出版年
2024
NETL
NSTL
万方数据