| 一类非线性三阶系统的全局渐近稳定性 |
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| 引用本文： | 夏清霞,;虞继敏,;穆春来.一类非线性三阶系统的全局渐近稳定性[J].广西师院学报,2009(3):26-29. |
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| 作者姓名： | 夏清霞 ;虞继敏 ;穆春来 |
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| 作者单位： | [1]广西师范学院数学科学学院,广西南宁530023; [2]重庆邮电大学数理学院,重庆400065; [3]重庆大学数理学院,重庆400044 |
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| 基金项目： | 广西教育厅科研处面上项目（200707ms063） |
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| 摘 要： | 针对非线性三阶系统x^…＋g（x^.）x^..＋f（x，x^.）x^.＋h（x）=p（x，^x.，^x..）构造出了一个适当的Lyapunov函数，并且去掉了一般要求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，所得结果改进了相关文献的结论．最后，文中给出了例子仿真说明充分条件的有效性．
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| 关 键 词： | 非线性系统 全局渐进稳定 Lyapunov函数 |
Globally Asymptotic Stability Analysis of a Class of Nonlinear Third- order Systems |
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| Institution: | XIA Qing-xia, YU Ji--min , Mu Chun-lai (1. School of Mathematical Sciences, Guangxi Teacher Education University, Nanning 530023, China; 2. College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; 3. College of Mathematics and Physics, Chongqing University, Chongqing 400044, China) |
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| Abstract: | For the nonlinear third order system x^…＋g（x^.）x^..＋f（x,x^.）x^.＋h（x）=p（x,^x.,^x..）, a better Lyapunov function is constructed in this paper, and the original stronger requirement is removed here as the Lyapunov function must trend to infinity, and there is only one need that the positive half orbit of the system is bounded. The results improve the conclusions of relevant literature. At last, the simulation of example shows the conditions for the effectiveness. |
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| Keywords: | nonlinear system globally asymptotic Lyapunov function |
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