引用本文:倪郁东,沈吟东.二维非线性临界解析动态系统的局部渐近稳定性[J].控制理论与应用,2009,26(2):179~182.[点击复制]
NI Yu-dong,SHEN Yin-dong.Locally asymptotic stability of 2-dimension nonlinear analytic dynamic systems in critical cases[J].Control Theory and Technology,2009,26(2):179~182.[点击复制]
二维非线性临界解析动态系统的局部渐近稳定性
Locally asymptotic stability of 2-dimension nonlinear analytic dynamic systems in critical cases
摘要点击 1829  全文点击 1172  投稿时间：2007-05-14  修订日期：2008-04-30
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DOI编号  10.7641/j.issn.1000-8152.2009.2.012
  2009,26(2):179-182
中文关键词  非线性动态系统  临界情形  李雅普诺夫函数  局部渐近稳定
英文关键词  nonlinear dynamic system  critical case  Lyapunov function  locally asymptotic stability
基金项目  国家自然科学基金资助项目(70671045).
作者单位E-mail
倪郁东 合肥工业大学 数学系, 安徽 合肥 230009 niyudong888@126.com 
沈吟东 华中科技大学 控制科学与工程系, 湖北 武汉 430074 yindong@mail.hust.edu.cn 
中文摘要
      考察具有一对共轭纯虚数特征值的二维非线性临界解析动态系统的局部渐近稳定性. 首先在非奇异线性坐标变换和时间尺度变换下, 将其化成标准形式. 之后, 运用形式级数法的思想, 通过构造多组线性方程组,给出了确定该系统的李雅普诺夫函数的方法, 并得到了判别系统局部渐近稳定和不稳定的充分条件. 最后通过示例说明该判别条件的有效性.
英文摘要
      The locally asymptotic stability of a 2-dimension nonlinear analytic dynamic system with a pair of conjugated imaginary eigenvalues is studied. The system is firstly simplified to a standard form by using the non-singular linear coordinate transformation and the time scale transformation. Next, based on the idea of formal progression, a method is developed to determine the Lyapunov function for this standard form by constructing several sets of linear equations. Finally, a sufficient condition of locally asymptotic stability for the system is obtained. The validity is shown by two examples at the end of this paper.