一类系统的二次李雅普诺夫函数存在性的判断  

Judgement on the existence of a common quadratic Lyapunov function for a kind of systems

作　　者：陈征[1] 

机构地区：[1]宁波工程学院基础部,浙江宁波315016

出　　处：《安徽电子信息职业技术学院学报》2006年第4期30-31,共2页Journal of Anhui Vocational College of Electronics & Information Technology

摘　　要：本文首先引入了系统矩阵为友阵的一对稳定的LTI系统的二次李雅普诺夫函数存在的充要条件.然后把此充要条件转换为判断实系数一元多项式方程的负实根个数是否为零的问题,并用实根分离算法对多项式方程系数为有理数的情况给出了具体的算法.最后给出了一些实例.In this paper, the necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time - invariant systems whose system matrices are in companion form are introduced. Then to judge the necessary and sufficient conditions is to decide whether polynomial equation with real coefficients has any negative real root, and the real root isolation for the polynomial equation with rational coefficients is given.. Examples are presented to illustrate the results.

关 键 词：友阵 李雅普诺夫函数 特征值 实根分离法 

分 类 号：O15[理学—数学]