G⁃Brown运动驱动的非线性随机时滞微分方程的稳定化  

Stabilization of Nonlinear Stochastic Delay Differential Equations Driven by G⁃Brownian Motion

作　　者：李光洁 杨启贵 LI Guangjie;YANG Qigui(School of Mathematics and Statistics,Guangdong University of Foreign Studies,Guangzhou 510006,P.R.China;School of Mathematics,South China University of Technology,Guangzhou 510640,P.R.China)

机构地区：[1]广东外语外贸大学数学与统计学院,广州510006 [2]华南理工大学数学学院,广州510640

出　　处：《应用数学和力学》2021年第8期841-851,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11901398,12071151)。

摘　　要：研究了一类G⁃Brown运动驱动的非线性随机时滞微分方程的稳定化问题.首先,在一个不稳定的G⁃Brown运动驱动的非线性随机时滞微分方程的漂移项中设计了时滞反馈控制,得其相应的控制系统.其次,利用Lyapunov函数方法给出其相应的控制系统是渐近稳定的充分条件.最后,通过例子说明了所得的结果.The stabilization problem of a class of nonlinear stochastic delay differential equations driven by G⁃Brownain motion(G⁃SDDEs)was studied.Firstly,a delay feedback control was designed in the drift term of an unstable nonlinear G⁃SDDE,and the controlled system was therefore obtained.Then,with the Lyapunov technique,sufficient conditions for the asymptotical stability of the controlled system were given.Finally,two examples were presented to illustrate the obtained results.

关 键 词：非线性随机时滞微分方程 时滞反馈控制 G⁃Brown运动 渐近稳定性 

分 类 号：O211.63[理学—概率论与数理统计]