随机自治系统的Lasalle定理的改进  

The Improve of Lasalle Theorem in Differential Autonomous System

作　　者：周树克[1] 李华[1] 张云贞[2] 

机构地区：[1]河南城建学院数理学院,河南平顶山467000 [2]南京理工大学电光学院,南京210094

出　　处：《数学的实践与认识》2014年第2期286-288,共3页Mathematics in Practice and Theory

摘　　要：稳定性问题是研究各类动态系统的最基本也是最重要的问题之一.稳定性理论已经积累了十分丰富的成果,将Lasalle定理应用到随机微分自治系统中构造具体的Lyapunov函数,得到随机自治系统渐近稳定的有用判据.最后具体实例来说明改进结果的有效性.As we all know,stability is the most basic study on all kinds of dynamic systems,and it is also one of the most important issues.Stability has accumulated a great wealth of results,this paper generalizes Lasalle theorem to stochastic differential autonomous system,contructs a Lyapunov function and extends a useful theorem about stochastic asymptotically stable for stochastic differential autonomous system.At last,we give concrete example to illustrate the theorems.

关 键 词：自治系统 渐近稳定 LYAPUNOV函数 Lasalle定理 不变集 

分 类 号：O211.6[理学—概率论与数理统计]