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.