Mean-square Exponential Input-to-state Stability of Euler-Maruyama Method Applied to Stochastic Control Systems

作     者：ZHU Qiao HU Guang-Da ZENG Li 

作者机构：Department of Automation Information Engineering SchoolUniversity of Science and Technology Beijing Beijing 100083 P.R.China 

出 版 物：《自动化学报》 (Acta Automatica Sinica)

年 卷 期：2010年第36卷第3期

页      面：406-411页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 0835[工学-软件工程] 0802[工学-机械工程] 070102[理学-计算数学] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported by National Natural Science Foundation of China(10571036) the Key Discipline Development Program of Beijing Municipal Commission (XK100080537) 

主　　题：均方指数 收敛性 连续随机函数 控制方法 

摘      要：This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions. Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coeffcients and mean-square continuous random inputs. Under the strong convergent condition,it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for suffciently small step size