带有输入时滞的线性系统的稳定性分析  

Stability analysis for linear systems with input-delay

作　　者：李丽[1] 王玉婷 LI Li;WANG Yuting(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4期350-353,共4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(LJKZ01007)。

摘　　要：针对一类带有输入时滞的线性系统,利用Lyapunov-Krasovskii泛函法,给出一个稳定性准则。首先,构造一个增广的非对称Lyapunov-Krasovskii泛函;其次,通过Wirtinger不等式对L-K泛函进行分析和估计,利用积分不等式和线性不等式进一步推导得到L-K泛函整体正定的条件和求导条件,又由于该系统带有输入时滞,对此引入零方程,得到以LMI形式表示的带有输入时滞的线性系统的稳定性准则;最后,利用数值算例,通过LMI工具箱求解,验证了所得结果的有效性和可行性。For a class of linear system with input delays,a stability criterion is given by using Lyapunov-Krasovskii functional method.Firstly,construct an augmented asymmetric Lyapunov-Krasovskii functional.Secondly,the L-K functional is analyzed and estimated through the Wirtinger inequality,and the conditions for the global positive definite and derivative of the L-K functional are obtained through the further derivation and transformation of the integral inequality and the linear inequality.Because the system has input delays,the Zero matrix is introduced to obtain the sufficient conditions for the stability of the linear system with input delays in the form of LMI.Finally,numerical examples are used to validate the effectiveness and feasibility of the obtained results through the LMI toolbox.

关 键 词：时变时滞系统 稳定性 LYAPUNOV-KRASOVSKII泛函 WIRTINGER不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]