Exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses via Razumikhin method

* Correspondence: [email protected]. cn Department of Mathematics, Southeast University, Nanjing 210096, P. R. China Full list of author information is available at the end of the article Abstract In this article, by using Razumikhin-type technique, we investigate pth moment exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses. Several stability theorems of impulsive hybrid stochastic functional differential equations are derived. It is assumed that the state variables on the impulses can relate to the finite delay. These new results are employed to a class of n-dimensional linear impulsive hybrid stochastic systems with bounded time-varying delay. Moreover, an effective M-matrix method is introduced to study the exponential stability of these hybrid systems. Meanwhile, some examples and simulations are given to show our results.