随机自治系统的Lasalle定理的改进

The Improve of Lasalle Theorem in Differential Autonomous System

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.