Stability of a class of stochastic switched systems with time delays

In this paper, the problem of stochastic switched systems with time delay is investigated. To study the existence of the solution to the switched system with time delay by means of Ito´s formula, it is critical to show switching moments as stopping times. For switching law caused by overlapping active regions, the solution of the switched system is constructed and a stability criterion of the equilibrium is presented. The significance of the work in this paper is that all the results depend on some easily-verified assumptions that are as elegant as those in the deterministic case.