对不确定脉冲随机系统的几乎必然指数稳定性和随机状态反馈镇定进行研究.考虑了三种不同作用的脉冲:镇定型的脉冲、干扰型的脉冲、中立型的脉冲. 利用Lyapunov函数和线性矩阵不等式工具,得到系统基于线性矩阵不等式形式的几乎必然指数稳定性判据,该判据表明若脉冲的强度和发生的频率与噪声强度及相应连续系统的增减速率相互协调,则系统的解可达到稳定状态.在稳定性分析的基础上,进一步研究了系统的随机状态反馈镇定问题.数值例子及仿真证明了文章方法的有效性.

This paper is concerned with the almost sure exponential stability and stochastic state feedback stabilization of uncertain stochastic systems with impulses. Three types of impulses are considered: Stabilizing impulses, destabilizing impulses and neutral impulses. By using the Lyapunov functions and linear matrix inequalities (LMIs) tool, the sufficient conditions for almost sure exponential stability criteria are derived in terms of LMIs, which show that the system will stable if the impulses' frequency and strength are suitably related to noise intensity, as well as the increase or decrease of the underlying continuous flows. Furthermore, the stochastic state feedback controllers that almost sure exponentially stabilize the uncertain impulsive stochastic systems are proposed. Finally, a numerical example is given to show the effectiveness of the results.