%0 Journal Article
%T Locally asymptotic stability of 2-dimension nonlinear analytic dynamic systems in critical cases<br>二维非线性临界解析动态系统的局部渐近稳定性
%A NI Yu-dong
%A SHEN Yin-dong
%A <br>倪郁东
%A 沈吟东
%J 控制理论与应用
%D 2009
%I 
%X 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.
%K nonlinear dynamic system
%K critical case
%K Lyapunov function
%K locally asymptotic stability<br>非线性动态系统
%K 临界情形
%K 李雅普诺夫函数
%K 局部渐近稳定
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=970898A57DFC021F93AB51667BAED7F7&aid=9072E637974C5332D0641624D00C5D59&yid=DE12191FBD62783C&vid=96C778EE049EE47D&iid=0B39A22176CE99FB&sid=E114CF9BB47B65BE&eid=B1F98368A47B8888&journal_id=1000-8152&journal_name=控制理论与应用&referenced_num=0&reference_num=9