Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching

In this paper, we are concerned with the stability analysis of stochastic nonlinear systems with delayed impulses and Markovian switching. Different from the previous literature, the impulses in this paper depend on delays and the jumping parameters are described by a continuous-time Markov chain with a finite-state space. Several novel stability criteria are obtained by using a stochastic Lyapunov function method and the Razumikhin technique. To be less conservative, the Razumikhin condition imposed on the coefficient of the estimated upper bound for the Lyapunov function's time-derivative is improved from a constant to a function, which can be either positive or negative. Finally, we use two examples and their simulations to verify the validity of the theory results.