非线性随机时滞微分系统的脉冲镇定（英文）  

Impulsive Stabilization of Nonlinear Stochastic Delay Differential Systems

作　　者：李殿强[1] 程培[1] 尚蕾[1] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《应用数学》2016年第4期826-836,共11页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11301004,61403002,61273126);the Anhui Provincial Nature Science Foundation(1308085QA15,1308085MA01,1508085QA01);the Excellent Youthful Talent Foundation of Colleges and Universities of Anhui Province of China(2013SQRL024ZD);the Postdoctoral Sus-tentation Fund of Jiangsu Province of China(1402021C);Provincial Natural Science Research Project of Anhui Colleges(KJ2014A010);Research Fund for Doctor Station of Ministry of Education of China(20113401110001)

摘　　要：本文研究一类非线性随机时滞微分系统的脉冲镇定.利用Lyapunov函数,Razumikhin和一些分析的技巧得到系统基于线性矩阵不等式形式的均方稳定性判据,该判据表明适当的脉冲可以用来镇定不稳定的随机时滞系统.与此同时,数值例子及仿真证明了本文方法的有效性.This paper mainly studies the problem of impulsive stabilization of nonlinear stochastic delay differential systems. By using Lyapunov functions, Razumikhin theorem and some analysis techniques, the sufficient conditions for mean square exponential stability are developed in terms of linear matrix inequalities（LMIs）, which shows that unstable stochastic delay systems may be stabilized by appropriate impulses. Meanwhile, two examples with numerical simulations are given to illustrate the effectiveness of the results obtained.

关 键 词：脉冲镇定 随机微分系统 时滞 均方稳定 LYAPUNOV函数 Razumikhin型技巧 线性矩阵不等式 

分 类 号：O231[理学—运筹学与控制论]