In this paper, the global asymptotic stability in probability and the exponential stability in $m$th moment are investigated for random nonlinear systems with stochastic impulses, whose occurrence is determined by a Poisson process. The stochastic disturbances in the impulsive random nonlinear systems are driven by second-order processes, which have bounded mean power. Firstly, the improved Lyapunov approaches for the global asymptotic stability in probability and the exponential stability in $m$th moment are established for impulsive random nonlinear systems based on the uniformly asymptotically stable function. Secondly, the improved results are further extended to the impulsive random nonlinear systems with Markovian switching. Finally, two examples are provided to verify the feasibility and effectiveness of the obtained results.

在本文中，概率的全局渐近稳定性和指数稳定性 $米$对于具有随机脉冲的随机非线性系统，研究了第 th 时刻，其发生由泊松过程确定。脉冲随机非线性系统中的随机扰动由二阶过程驱动，二阶过程具有有界平均功率。首先，改进的 Lyapunov 方法用于概率的全局渐近稳定性和指数稳定性$米$为基于一致渐近稳定函数的脉冲随机非线性系统建立了第 th 矩。其次，将改进的结果进一步推广到具有马尔可夫切换的脉冲随机非线性系统。最后通过两个例子验证所得结果的可行性和有效性。