Input-to-state stability analysis of stochastic delayed switching systems

In this paper, the issues regarding the input-to-state stability (ISS) and integral input-to-state stability (iISS) of the stochastic delayed switching systems with Lévy noise and input control (SDSS-LN-IC) are proposed by employing the comparison theorem approach, mode-dependent average dwell time (MDADT) method, delay integral inequality (DII), and Lyapunov-Razumikhin (L-R) technique. Two switching situations, namely, synchronous switching and asynchronous switching, are considered. Applying integral inequalities, sufficient stability conditions in both cases are given. Moreover, the sequences of this paper allow for the coefficients for the upper-bound expectation estimation of the infinitesimal operator to be mode-dependent, regardless of the sign and time-varying function rather than a constant, as is the case in certain existing results, which manifests the condition of the Lyapunov-Razumikhin technique in this paper is looser and less conservative. Finally, the validity and correctness of the theoretical results are verified by two examples and some simulations.