非线性中立型随机微分系统的稳定性  

Stability of Nonlinear Stochastically Differential Systems in Neutral Type

作　　者：刘宏亮[1,2] 段广仁[2] 

机构地区：[1]哈尔滨师范大学数学科学学院,黑龙江哈尔滨150025 [2]哈尔滨工业大学控制理论与指导技术中心,黑龙江哈尔滨150001

出　　处：《数学的实践与认识》2011年第11期209-215,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(51002041);黑龙江省教育厅教育项目(11551134);哈尔滨师范大学项目基金(KGB200911;10XYG-06)

摘　　要：研究了一类非线性中立型随机微分系统的稳定性问题.该类非线性随机微分系统不仅包含系统的过去状态,而且还和系统的过去时刻的运动特性相关,同时,还具有Markov跳变参数.利用所定义的广义Ito微分公式,通过构造适当随机Lyapunov泛函,给出了此类随机系统的均方指数稳定性的充分条件.该条件放宽了已有结果的限制,具有更加广泛的适用范围.同时,还给出了此类随机系统的几乎必然指数稳定性的充分条件.Stability of Nonlinear Stochastically Differential Systems in Neutral Type was dis- cussed in this paper. Such systems contain the past states of the systems and the derivation of past states,and posses parameters with Markov switching. By defined Generalized Ito formula, and constructing proper stochastic Lyapunov functional, the sufficient condition is proposed for the mean square exponential stability of such systems, which is less constrains than existed conditions. And, the sufficient condition is proposed for the almost sure exponential stability of such systems.

关 键 词：随机微分系统 MARKOV跳变 中立型系统 随机稳定性 广义Ito公式 

分 类 号：O211.6[理学—概率论与数理统计]