On input-to-state stability of switched stochastic nonlinear systems under extended asynchronous switching

An extended asynchronous switching model is investigated for a class of switched stochastic nonlinear retarded systems in the presence of both detection delay and false alarm, where the extended asynchronous switching is described by two independent and exponentially distributed stochastic processes, and further simplified as Markovian. Based on the Razumikhin-type theorem incorporated with average dwell-time approach, the sufficient criteria for global asymptotic stability in probability and stochastic input-to-state stability are given, whose importance and effectiveness are finally verified by numerical examples.