具有分布时滞的非线性广义系统一致渐近稳定性准则  

Uniformly asymptotic stability criterion for a class of nonlinear descriptor systems with distributed delay

作　　者：孙欣[1] 李俊欣 SUN Xin;LI Junxin(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）》2023年第1期36-44,共9页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究经费项目(LJC202002)。

摘　　要：针对一类具有分布时滞的非线性广义系统,利用李雅普诺夫第二方法和广义系统的受限等价变换,给出一致渐近稳定性准则。首先,在假设具有分布时滞的非线性广义系统是正则、无脉冲的基础上,构造了新的增广Lyapunov-Krasovskii泛函(L-K泛函),在L-K泛函中加入了三重积分项以获得更多的时滞信息;然后,对L-K泛函求导后产生的积分项应用边界估值更为精确的Bessel-Legendre不等式(B-L不等式)进行处理,利用Lyapunov稳定性理论和线性矩阵不等式给出了具有分布时滞的非线性广义系统的一致渐近稳定性准则条件;最后,利用数值算例,通过Matlab中LMI工具箱求解,验证了所用方法的可行性和有效性。The uniformly asymptotic stability criterion for a class of nonlinear descriptor systems with distributed delays is discussed by Lyapunov s second method and the limited equivalent transformation of descriptor systems.Firstly,under the assumption that the nonlinear descriptor system with distributed delay is regular and impulse free,a novel augmented Lyapunov-Krasovskii functional(L-K functional)is constructed in which the additional delay information is obtained by adding the triple integral terms into L-K functional.Secondly,the integral term produced by derivation of L-K functional is treated by Bessel Legendre inequality(B-L inequality)with more accurate boundary estimation.Consequently,the uniformly asymptotic stability criterion for a class of nonlinear descriptor systems with distributed delays is obtained by applying Lyapunov stability theory in terms of linear matrix inequality.Finally,a numerical example is provided to demonstrate feasibility and validity of the proposed method by virtue of the LMI toolbox of Matlab.

关 键 词：非线性广义系统 分布时滞 一致渐近稳定性准则 LYAPUNOV-KRASOVSKII泛函 Bessel-Legendre不等式 

分 类 号：O231[理学—运筹学与控制论]