Stability analysis for switched stochastic delayed systems under asynchronous switching: A relaxed switching signal

Summary This article deals with the stochastic input‐to‐state stability (SISS) for a class of switched stochastic systems under asynchronous switching. Asynchronous switching refers to that the switching of the candidate controllers does not coincide with the switching of system modes. In addition, the time delays appear in the state. Unlike the existing works, we not only allow the coefficients of the estimated upper bound for the diffusion operator of a Lyapunov function to be increasing during the matched time interval, but also in the unmatched time interval. Meanwhile, by using the switching signals which prevail over the traditional average dwell time scheme and the Razumikhin theorem, the SISS property is obtained. Especially our results improve some existing ones regarding asynchronous switching in the literature. Two examples are used to demonstrate the applicability of the results.