含非线性项的不确定离散时滞系统鲁棒稳定性分析  

Robust stability analysis of uncertain discrete time-delay systems with nonlinear terms

作　　者：孙延修[1] 潘斌[2] Sun Yanxiu;Pan Bin(Basic Course Department,Shenyang Institute of Technology,Fushun 113122,China;College of Science,Liaoning Shihua University,Fushun 113001,China)

机构地区：[1]沈阳工学院基础课部,辽宁抚顺113122 [2]辽宁石油化工大学理学院,辽宁抚顺113001

出　　处：《纯粹数学与应用数学》2021年第2期218-226,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(61602228);辽宁省教育厅科学研究项目(L201906).

摘　　要：针对一类同时存在非线性项和不确定项的离散时滞系统,研究了系统的鲁棒稳定性问题.通过构造Lyapunov函数并利用Schur补引理以线性矩阵不等式(LMI)形式给出了系统鲁棒稳定的充分条件;利用离散时滞系统鲁棒稳定性的充分条件,采用LMI技术,设计出基于LMI的状态反馈鲁棒控制器;理论证明该方法设计的控制器保证闭环系统鲁棒渐近稳定.For a class of discrete time-delay systems with both nonlinear and uncertain terms,the problem of robust stability is studied.The sufficient conditions for robust stability of the system are given in the form of LMI by constructing Lyapunov function and Schur complement lemma;the state feedback robust controller is designed by using linear matrix inequality(LMI)technique based on the sufficient conditions of robust stability of discrete time-delay systems;it is theoretically proved that the controller designed by this method guarantees the robust asymptotic stability of the closed-loop system.

关 键 词：非线性项 线性矩阵不等式(LMI) 状态反馈 离散时滞系统 

分 类 号：O23[理学—运筹学与控制论]