一类高阶随机非线性时变时滞系统的状态反馈控制  

STATE FEEDBACK CONTROL FOR STOCHASTIC NONLINEAR SYSTEMS WITH HIGH-ORDER TERMS AND TIME-VARYING DELAY

作　　者：井青翠 王天成 JING Qing-cui;WANG Tian-cheng(School of Mathematics and Statistics Science,Ludong University,Yantai 264025,China)

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264025

出　　处：《数学杂志》2020年第3期301-313,共13页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(61573179)。

摘　　要：本文研究了一类高阶随机非线性时变时滞系统的状态反馈控制问题.通过构造恰当的李雅普诺夫泛函,并结合随机系统的稳定性理论,获得了一个能使整个闭环系统为依概率全局渐近稳定的状态反馈控制器.本文系统具有更一般的高阶项,推广了以往单一高阶项系统依概率全局渐近稳定的结果.数值仿真验证了所提状态反馈控制器方案的有效性.In this paper,we study the state feedback control problem for a class of highorder stochastic nonlinear systems with time-varying delay.Using the Lyapunov method,a suitable Lyapunov functional is constructed and combined with the stability theory of stochastic systems,we obtain a state feedback controller which can make the global asymptotical stability(GAS)in probability of the closed-loop system.System in this paper has more general high-order terms,which generalizes the previous result of global asymptotic stability in probability of a single highorder term system.The efficiency of the state-feedback controller is demonstrated by a simulation example.

关 键 词：高阶项 时变时滞 状态反馈 Lyapunov-Krasovskii理论 随机非线性 

分 类 号：O231.3[理学—运筹学与控制论]