Sufficient conditions on finite‐time input‐to‐state stability of nonlinear stochastic impulsive time‐varying systems

Abstract

SummaryThe finite‐time input‐to‐state stability () of stochastic impulsive time‐varying nonlinear systems is investigated in this paper. Different from the previous works concerning , we allow the coefficients of the estimated upper bound for the diffusion operator of a Lyapunov function to be time‐varying. Moreover, a relaxed relation between the impulsive frequency is provided. Leveraging the Lyapunov method along with Lambert function and average impulsive interval () method, the input‐to‐state () property is obtained within finite time. Furthermore, two examples are provided to verify the validity of the conclusion.