| 一类三阶非线性系统的全局渐近稳定性 |
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| 引用本文： | 张丽娟,斯力更.一类三阶非线性系统的全局渐近稳定性[J].应用数学学报,2007,30(1):99-103. |
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| 作者姓名： | 张丽娟 斯力更 |
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| 作者单位： | 1. 烟台大学数学与信息科学系,烟台,264005
2. 内蒙古师范大学数学科学学院,呼和浩特,010020 |
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| 基金项目： | 国家自然科学基金;烟台大学校科研和教改项目 |
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| 摘 要： | 在运用Lyapunov函数第二方法研究非线性系统稳定性的时候,能否做出合适的Lya- punov函数是问题的关键,本文对三阶非线性系统x g(x)x f(x,x) h(x)=0构造出了较好的Lyapunov函数,得到其零解全局渐近稳定的充分性准则,它包含并改进了这一形式非线性系统的大部分结果．
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| 关 键 词： | 非线性系统 全局渐近稳定 Lyapunov函数 |
| 修稿时间： | 2005-04-13 |
Globally Asymptotic Stability of a Class of Third Order Nonlinear System |
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| ZHANG LIJUAN,SI LIGENG.Globally Asymptotic Stability of a Class of Third Order Nonlinear System[J].Acta Mathematicae Applicatae Sinica,2007,30(1):99-103. |
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| Authors: | ZHANG LIJUAN SI LIGENG |
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| Institution: | Department of Mathematics and Information Science, Yantai University, Yantai 264005;College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010020 |
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| Abstract: | It is critical to construct a suitable Lyapunov function in the study of the stability of nonlinear system by Lyapunov's second method. In this paper, a better Lyapunov function of third order nonlinear system x g(x) x f(x, x) h(x) = 0 is constructed, and some sufficient conditions are given ensuring globally asymptotic stability of the zero solution of the system. The work includes and improved a majority of results in the references. |
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| Keywords: | nonlinear system globally asymptotic stability Lyapunov function |
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