| 两类三阶非线性系统零解的全局渐近稳定性 |
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| 引用本文： | 蒋自国. 两类三阶非线性系统零解的全局渐近稳定性[J]. 四川师范大学学报(自然科学版), 2011, 34(2): 217-220. DOI: 10.3969/j.issn.1001-8395.2011.02.016 |
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| 作者姓名： | 蒋自国 |
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| 作者单位： | 阿坝师范高等专科学校数学系,四川,成都,611741 |
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| 基金项目： | 四川省教育厅自然科学重点基金 |
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| 摘 要： | 对三阶非线性系统x+g(x,)+f(x,)+h(x)=0和…x+g(x,)+f(x,)+h(x)=p(x,,)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.去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界,所得结果包含并改进了原有的结果.
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| 关 键 词： | 非线性系统 全局渐近稳定 Lyapunov函数 |
Globally Asymptotic Stability of Two Classes of Third-order Nonlinear Systems |
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| JIANG Zi-guo. Globally Asymptotic Stability of Two Classes of Third-order Nonlinear Systems[J]. Journal of Sichuan Normal University(Natural Science), 2011, 34(2): 217-220. DOI: 10.3969/j.issn.1001-8395.2011.02.016 |
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| Authors: | JIANG Zi-guo |
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| Affiliation: | JIANG Zi-guo(Department of Mathematics,Aba Teachers College,Chengdu 611741,Sichuan) |
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| Abstract: | For two classes of third order nonlinear systems x+g(x,)+f(x,)+h(x)=0 and x+g(x,)+f(x,)+h(x)=p(x,,),the better Lyapunov functions are constructed in this paper.By using these functions,some new sufficient conditions for globally asymptotic stability are obtained.The present results include and improve some old ones,since the original stronger requirement is removed here that the Lyapunov function must trend to infinity,and there is only one need that the positive half orbit of the system is bounded. |
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| Keywords: | nonlinear system globally asymptotic stability Lyapunov function |
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