中文摘要：

研究了一类随机混沌系统的几乎必然指数稳定性和随机噪声镇定问题.首先,利用Lyapunov函数法,得到了系统分别基于线性矩阵不等式和矩阵不等式形式的几乎必然指数稳定的判据.其次,在随机混沌系统稳定性分析的基础上,给出随机镇定的代数判据.最后,通过数值仿真验证了结论的有效性。

英文摘要：

This paper deals with the problem of almost sure exponential stability and stochastic stabilization of a class of stochastic chaotic system. By using Lyapunov functions, the sufficient conditions for almost sure exponential stability are developed in terms of linear matrix inequality and inequality matrix respectively. Then, on the basis of stability analysis, the algebraic criterion of stochastic stabilization is proposed. A numerical example is given to show the effectiveness of the obtained results.