| 随机自治系统的Lasalle定理的改进 |
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| 引用本文： | 周树克,李华,张云贞.随机自治系统的Lasalle定理的改进[J].数学的实践与认识,2014(2). |
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| 作者姓名： | 周树克 李华 张云贞 |
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| 作者单位： | 河南城建学院数理学院;南京理工大学电光学院; |
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| 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.
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| 关 键 词： | 自治系统 渐近稳定 Lyapunov函数 Lasalle定理 不变集 |
The Improve of Lasalle Theorem in Differential Autonomous System |
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| Abstract: | 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 weajth 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. |
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| Keywords: | autonomous system asymptotically stable Lyapunov function lasalle theorem involutive set |
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