引用本文:李春文，张平，乔岩.一类二维临界非线性系统的稳定性判别*[J].控制理论与应用,1998,15(6):842~846.[点击复制]
LI Chunwen， ZHANG Ping and QIAO Yan.Sufficient Conditions for Stability of a Class ofTwo-Dimensional Critical Nonlinear ystems[J].Control Theory & Applications,1998,15(6):842~846.[点击复制]
一类二维临界非线性系统的稳定性判别*
Sufficient Conditions for Stability of a Class ofTwo-Dimensional Critical Nonlinear ystems
摘要点击 1513  全文点击 617  投稿时间：1997-01-29  修订日期：1997-10-30
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DOI编号  
  1998,15(6):842-846
中文关键词  稳定性  正则判别函数法  临界系统
英文关键词  stability  normal determinative function method  critical system
基金项目  
作者单位
李春文，张平，乔岩 清华大学自动化系 
中文摘要
      利用一种判别系统稳定性的定号导函数方法——正则判别函数法，结合Normal Form 理论，对二维三次非线性系统的两种临界情形进行了稳定性分析，即对含一对纯虚根和含几何重数为一的两个零根的纯临界系统，分别给出了一组系统稳定的充分条件，并给出了相应的李亚普诺夫函数的形式.
英文摘要
      This paper analyses the stability of two-dimensional three-degree critical nonlinear tsyzstenrs. by using the Normal Determinative Function Method，which is a definite derivative function method to judge Lyapunov stability of systems. Two cases are considered，where the pure critical system has a pair of nonzero pure imaginary eigenvalues and two zero eigenvalues with geometric multiplicity one. For each system，the sufficient conditions for stability and the form of Lyapunov function are given.