Pth moment input-to-state stability of impulsive stochastic functional differential systems with Markovian switching

The paper introduces a unified criterion for pth moment input-to-state stability (p-ISS), pth moment integral input-to-state stability (p-iISS), and e^σt-weighted pth moment integral input-to-state stability (e^σt-p-ISS) of impulsive stochastic function differential system with Markovian switching under the perturbation of the stabilizing impulse and destabilizing impulse. The Lyapunov function approach, comparison principle, and impulsive average dwell-time method are applied in this paper. The linear coefficients of the upper bound of Lyapunov functional differential operators are time-varying functions, including the case of constants, which advances and improves the existing results. In addition, the same results were obtained by applying impulse differential inequality. At the end of this paper, we use a numerical example to verify the validity of the results.