线性随机时变系统的有限时间稳定性研究

Research on Finite Time Stability of Linear StochasticTime-varying System

针对一类具有有限时间的随机微分时变系统,研究了关于随机线性时变系统的有限时间稳定性及控制器设计问题。首先,引入了有限时间稳定性的定义,基于该定义提出了一种针对假定的L yapunov函数满足分段连续性,在每一个分段点处可能不连续的有限时间稳定性的新方法,并借助切换系统的思想研究了随机时变系统的有限时间稳定性;在此基础上,考虑带有反馈控制器的随机时变系统的控制器设置问题,并通过采用逐段控制的方法给出了系统的控制器设置方法;最后基于线性矩阵不等式设计了一类线性随机时变系统的有限时间稳定控制器的算法,使得对于控制器的设置能够有效地实现。

For a class of stochastic differential systems with finite time,the finite time stability and controller design of stochastic linear time-varying systems are studied.First,the definition of finite-time stability is introduced.Based on this definition,a new method for finite-time stability where the assumed Lyapunov function satisfies piecewise continuity and may be discontinuous at each piecewise point is proposed.With the help of the idea of switching systems,the finite time stability of stochastic time-varying systems is studied.Then,based on the finite time stability of the stochastic time-varying system,the controller setting problem of the stochastic time-varying system with feedback controller is considered,and the system controller setting method is given by adopting the step-by-step control method.Finally,based on the linear matrix inequality,a class of linear stochastic time-varying system′s finite time stable controller algorithm is designed,so that the setting of the controller can be effectively realized.