Exponential stability conditions for switched stochastic systems with statedelay

The switched systems composed of several linear It?o 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.