Stability analysis of a class of hybrid stochastic retarded systems under asynchronous switching

The stability of a class of hybrid stochastic retarded systems (HSRSs) with an asynchronous switching controller is investigated. In this model, the controller design relies on the observed jumping parameters, which are however delayed and thus can not be measured in real-time precisely. This delayed time interval, referred to as the 'asynchronous switching interval', is Markovian and dependent on the actual switching signal. The sufficient conditions under which the system is either stochastically asymptotic stable or input-to-state stable are obtained by applying the extended Razumikhin-type theorem to the asynchronous switching interval. These results are less conservative as it is only required that the designed Lyapunov function is non-decreasing. It is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying Markov process, which is a conclusion similar to that in asynchronous deterministic switched systems. The effectiveness and correctness of the obtained results are finally verified by a numerical example.