pth Moment Exponential Stability of Impulsive Stochastic Functional Differential Equations

This paper centers on the exponential stability of impulsive stochastic functional differential equations. We give two related theorems. Initially, in the first theorem, we introduce a generalized Halanay inequality and use this generalized Halanay inequality to prove that impulsive stochastic functional differential equations are exponentially stable. Subsequently, in the second theorem, by Lyapunov second method, we obtain the exponential stability result for impulsive stochastic functional differential equations. Finally, the generalization and effectiveness of the results obtained are demonstrated through two examples.