关于李雅普诺夫函数最优性的探讨

给出了常系数线性系统李雅普诺夫函数最优性的一种定义，针对特征根本为实单根以及特征根具有共轭复根等情况，分别给出用二次型写出的最优李雅普诺夫函数公式。算例表明，用最优李雅普诺夫函数获得的吸引区域，较其它李雅普诺夫函数获得的吸引区域，更接近系统的真实的吸引区域。

Study of Optimality of Lyapunov Functio

his peper preliminarily diScusses the optimality of Lyapunov function for linear systems with constant asefficients. First of all,it gives a definition of Optimality.Then,for the case that the characteristic roots are all real single roots and have conjugate complex roots,the optimal formulas of Lyapunov function are written in a qtladratic fOrm. Finally, a prac-tical example is given to reveal that the domain of attraction obtained by the optimal Lya-punov function is clewr to the real domain of attraction for linear systems than that obtained by otherLyapunov functions.