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The paper mainly studies globally  p th moment exponentially ultimate boundedness and  p th moment exponential stability of impulsive stochastic functional differential equations. By using the Lyapunov direct method of Razumikhin-type condition and principle of comparison, this article first gives a lemma, discusses the simple system that does not consider impulse in the original system, then directly apply the conclusion of the lemma and use mathematical induction to get the main results of the theorem.  In this paper, when allowing the original system to be unbounded and unstable, some sufficient conditions for  p th moment globally exponentially ultimate boundedness and  p th moment globally exponential stability are presented, and the linear coefficient of the upper bound of Lyapunov differential operator is time-varying function, and is not required to be negative definite. Finally, we use an example to illustrate the validity of our results.

Exponential ultimate boundedness and stability of impulsive stochastic functional differential equations