pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs

Abstract This paper investigates the p th moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the p th moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the p th moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained.

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