随机控制系统Euler-Maruyama方法的均方指数输入状态稳定性

分析了随机控制系统Euler-Maruyama (EM)方法的均方指数输入状态稳定性. 本文的目的是寻找随机控制系统和EM方法分享它们均方指数输入状态稳定性的条件. 在全局Lipschitz系数和均方连续随机输入的基础上, 二阶矩的界和合适形式的强收敛条件被得到了. 在该强收敛条件下, 我们证明了一个随机控制系统是均方指数输入状态稳定的, 当且仅当对充分小的步长, EM方法也是均方指数输入状态稳定的.

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

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 coefficients 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 sufficiently small step size.