Input-to-state stability for non-linear switched stochastic delayed systems with asynchronous switching

In this study, the input-to-state stability (ISS), stochastic-ISS and integral-ISS problems for a class of switched stochastic systems with time delays are studied. A continuously differentiable Lyapunov-Krasovskii function with an indefinite derivative is employed to derive the ISS-type properties of the systems. Two cases are considered: (i) synchronous switching, i.e. candidate controllers coincide with the switching of the system mode; (ii) asynchronous switching, i.e. the candidate controllers have a lag to the switching of the system modes. Furthermore, for asynchronous switching, the authors allow the Lyapunov-Krasovskii function to be time-varying and increasing, respectively, during the time when the active subsystem and the controller match each other. Then, by means of the average dwell-time method together with the Lyapunov-Krasovskii function, they can get the desired ISS-type results. Finally, two examples are given to show the validity of the results.