Asymptotic stability for a class of switched stochastic delayed differential systems

Several novel p$$ p $$th moment asymptotic stability criteria are established for switched stochastic delayed differential systems (SSDDSs) under the framework that the time-delay is unbounded. These criteria are obtained by constructing some special sets and using the Lyapunov function approach. The features of the criteria show that the form of the unbounded delay plays an important role in keeping the stability of the related systems. As a corollary, if the number of subsystems is only one, the system is reduced to stochastic delayed differential systems (SDDSs), and the criterion of the p$$ p $$th moment asymptotic stability for this system is also obtained, which can improve the existing results for SDDSs with unbounded delays. Finally, two numerical examples are given to show the significance of our results.