具有时变时滞中立型Lur’e系统的绝对稳定性判据  

Absolute stability criterion for neutral-type Lur'e systems with time-varying delay

作　　者：孙欣[1] 李浩铭 SUN Xin;LI Haoming(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报(自然科学版)》2025年第1期62-69,共8页Journal of Shenyang Normal University:Natural Science Edition

基　　金：2022年度辽宁省教育厅普通高等教育本科教学改革研究项目;辽宁省教育厅高校基本科研项目(JYTMS20231698);辽宁省属本科高校基本科研业务费研究生专项资金资助项目(SYNUSJ2024014)。

摘　　要：针对一类具有时变时滞的中立型Lur'e系统,基于李雅普诺夫第二方法,结合最优划分延迟区间技术,提出了绝对稳定性判据。首先,通过引入可调参数α,将离散时滞区间划分为2个部分;其次,通过选取增广型一重积分Lyapunov-Krasovskii(L-K)泛函,引入2个松弛的矩阵变量,构造双重积分L-K泛函,从而使L-K泛函中包含更多时滞信息;再次,应用Wirtinger积分不等式、双重积分不等式和一种新的互凸组合方法对L-K泛函求导后产生的积分项进行处理,得出具有时变时滞的中立型Lur'e系统的绝对稳定性条件;最后,利用Matlab中的LMI工具箱,通过数值算例验证所提出方法的可行性和有效性。Based on Lyapunov s second method and the optimally dividing delay interval technique,an absolute stability criterion for a class of neutral-type Lur'e systems with time-varying delays is proposed.Firstly,by introducing an adjustable parameterα,the interval of discrete delay is divided into two parts.Secondly,an augmented single integral Lyapunov-Krasovskii(L-K)functional is selected,and two relaxed matrix variables are introduced to construct double integral L-K functionals in which the additional delay information is obtained.Then,the integral term producted by derivation of L-K functional is dealt with by utilizing Wirtinger integral inequality,double-integral inequalities and a new reciprocally convex method.Thereby,an absolute stability condition for the neutral-type Lur'e system with time-varying delays is obtained.Finally,a numerical example is provided to demonstrate the feasibility and effectiveness of the proposed method via the LMI toolbox in Matlab.

关 键 词：中立型Lur'e系统 绝对稳定性 最优划分延迟区间 松弛矩阵变量 互凸组合方法 

分 类 号：O231[理学—运筹学与控制论]