Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses

•A class of more generalized impulsive stochastic functional differential systems with delayed impulse.•Stable continuous stochastic dynamics/unstable discrete dynamics.•Unstable continuous stochastic dynamics/stable discrete dynamics.•pth Moment exponential stability and almost exponential stability.•The system will stable if impulses are suitably related to continuous flows.

This paper is concerned with the exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses. Although the stability of impulsive stochastic functional differential systems have received considerable attention. However, relatively few works are concerned with the stability of systems with delayed impulses and our aim here is mainly to close the gap. Based on the Lyapunov functions and Razumikhin techniques, some exponential stability criteria are derived, which show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows. The obtained results improve and complement ones from some recent works. Three examples are discussed to illustrate the effectiveness and the advantages of the results obtained.