This paper aims to analyze the behavior of the solutions of a stochastic perturbed system with respect to the solutions of the stochastic unperturbed system. To prove our stability results, we have derived a new Gronwall-type inequality instead of the Lyapunov techniques, which makes it easy to apply in practice and it can be considered as a more general tool in some situations. On the one hand, we present sufficient conditions ensuring the global practical uniform exponential stability of SDEs based on Gronwall’s inequalities. On the other hand, we investigate the global practical uniform exponential stability with respect to a part of the variables of the stochastic perturbed system by using generalized Gronwall’s inequalities. It turns out that, the proposed approach gives a better result comparing with the use of a Lyapunov function. A numerical example is presented to illustrate the applicability of our results.

本文旨在分析随机扰动系统的解相对于随机未扰动系统的解的行为。为了证明我们的稳定性结果，我们推导了一种新的 Gronwall 型不等式而不是 Lyapunov 技术，这使得它很容易在实践中应用，并且在某些情况下可以被认为是更通用的工具。一方面，我们提出了充分的条件，确保基于 Gronwall 不等式的 SDE 的全局实际一致指数稳定性。另一方面，我们利用广义Gronwall不等式研究了随机扰动系统的部分变量的全局实用均匀指数稳定性。事实证明，与使用 Lyapunov 函数相比，所提出的方法给出了更好的结果。