新的广义时滞系统容许性条件  

A new admissibility condition for descriptor delay systems

作　　者：孙欣[1] 王瀚萱 SUN Xin;WANG Hanxuan(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）》2024年第2期164-171,共8页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅高校基本科研项目(JYTMS20231698).

摘　　要：针对广义时滞系统,基于李雅普诺夫第二方法和广义系统的受限等价变换,结合积分不等式技术,给出一个线性矩阵不等式(linear matrix inequality,LMI)形式的容许性条件。首先,利用广义系统的受限等价变换得出广义时滞系统是正则且无脉冲的;然后,通过选取增广型Lyapunov-Krasovskii泛函(L-K泛函)和多重积分型L-K泛函,引入松弛型L-K泛函构建新的L-K泛函,利用Jensen积分不等式和Wirtinger积分不等式对L-K泛函求导后产生的积分项进行处理,得出广义时滞系统的稳定性条件,进而得到广义时滞系统的容许性条件;最后,利用MATLAB中的LMI工具箱,通过数值算例验证所用方法的可行性和有效性。Based on Lyapunov′s second method and limited equivalent transformations of descriptor systems,combined with the integral inequality technique,an admissibility condition for descriptor delay systems is given in the form of linear matrix inequality(LMI).Firstly,it is concluded that the descriptor delay system is regular and impulse free by using limited equivalent transformations of descriptor systems.Secondly,a new Lyapunov-Krasovskii functional(L-K functional)is constructed by selecting the augmented L-K functional,multiple integral L-K functional and introducting the relaxed L-K functional,and then,the integral terms producted by derivation of L-K functional are dealt with by Jensen integral inequality and Wirtinger integral inequality,respectively.Thus,a stability condition for the descriptor delay system is obtained,correspondingly,an admissibility condition for the descriptor delay system is obtained.Finally,a numerical example is provided to demonstrate feasibility and validity of the proposed method by virtue of LMI toolbox of MATLAB.

关 键 词：广义时滞系统 容许性条件 LYAPUNOV-KRASOVSKII泛函 Jensen积分不等式 Wirtinger积分不等式 

分 类 号：O231[理学—运筹学与控制论]