Exponential Stability of Impulsive Neutral Stochastic Functional Differential Equations

This paper focuses on the problem of the pth moment and almost sure exponential stability of impulsive neutral stochastic functional differential equations (INSFDEs). Based on the Lyapunov function and average dwell time (ADT), two sufficient criteria for the exponential stability of INSFDEs are derived, which manifest that the result obtained in this paper is more convenient to be used than those Razumikhin conditions in former literature. Finally, two numerical examples and simulations are given to verify the validity of our result.

Automated summary

This paper focuses on the problem of pth moment and almost sure exponential stability of impulsive neutral stochastic functional differential equations (INSFDEs). Two sufficient criteria for the exponential stability of INSFDEs are derived based on Lyapunov function and average dwell time (ADT), which are more convenient to be used than the Razumikhin conditions in previous literature.