The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic systems, in particular, of singular stochastic systems. The main objective of the paper is the analysis of the stability of stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. The uniform exponential stability in mean square and the practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems based on Lyapunov techniques are investigated. Moreover, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, an illustrative example is given to illustrate the effectiveness of the proposed results.

Lyapunov函数的方法是研究随机系统（尤其是奇异随机系统）稳定性的最有效方法之一。本文的主要目的是在假设初始条件一致的情况下，使用Lyapunov技术分析随机扰动奇异系统的稳定性。研究了基于Lyapunov技术的随机扰动奇异系统解的均方根均匀指数稳定性和均方根实际均匀指数稳定性。此外，我们研究了几类随机奇异系统的稳定性和稳定性问题。最后，给出一个说明性的例子来说明所提出的结果的有效性。