具有状态时滞的切换随机系统的指数稳定条件

Exponential stability conditions for switched stochastic systems with statedelay

考虑由具有状态时滞的线性Ito随机子系统构成的切换系统,基于多Lyapunov泛函方法研究切换与时滞对于稳定性的共同影响,并以此建立均方指数稳定条件.在均方意义下噪声对于稳定性的影响基本是负面的,因此构造一类形式较为一般的Lyapunov泛函并运用噪声的统计特性于其解析过程中,以减少噪声所引起的保守性.最后,通过一个仿真算例描述切换与时滞的相互制约关系表明了所提出方法的有效性.

The switched systems composed of several linear Ito stochastic subsystems with time-delay are considered.Based on the multiple Lyapunov functionals approach,the joint effects of switching and time-delay on stability are investigated so as to establish exponential stability conditions in the mean square sense.As noise in principle plays a negative role in preserving stability in the mean square sense,its statistic property is combined into computing a kind of Lyapunov functional,which is in a rather general form,to reduce the conservatism caused by noise itself.A simulation example is given to describe the mutually constraint relation between switching and time-delay,and illustrate the effectiveness of the proposed method.