Exponential stability for generalized stochastic impulsive functional differential equations with delayed impulses and Markovian switching

This paper is concerned with exponential stability for a class of generalized stochastic impulsive functional differential equations with delayed impulses and Markovian switching. A novel subsequence approach of the impulsive and switching time sequence is introduced to cope with the impulsive control problem with large and small delays. Based on the stochastic Lyapunov function and Razumikhin technique, a dwell time bound and related criteria are established to ensure the pth moment exponential stability, almost surely exponential stability and uniform stability of the trivial solutions. The main advantage of the proposed algorithm lies in that the delay bound and parameters are not necessarily required, which are commonly used to restrict the dwell-time bound and the decay rate of Lyapunov function. Finally, two examples are performed to demonstrate the usefulness of the main results.