非线性系统零解稳定性判定的广义二次型方法

为了寻找一种能充分利用矩阵理论构造非线性系统李亚普诺夫函数的方法．首先提出分量函数矩阵和广义二次型函数等概念，得到了如果一个函数的导数具有某种特定形式。则不需处理旋度方程．便可直接得到该函数的若干定理；然后提出一种构造李亚普诺夫函数和判定非线性系统零解稳定性的广义二次型方法．并举例说明了该方法的应用．理论和实例表明，该方法是一种充分利用矩阵特性，适用范围广且不需处理旋度方程的方法．

Generalized quadratic form method for zero-solution stability of nonlinear systems

In order to take advantage of matrix for constructing Lyapunov function of nonlinear systems,some conceptions,such as element function matrix and generalized quadratic form function,are proposed.The corresponding theorems are then proofed,in which if a function's derivative has a certain form,then the function could be directly concluded without dealing with rotation equations.Finally,a method of constructing Lyapunov function,so called generalized quadratic form method,is presented for zero-solution stability criterion of nonlinear systems.An example indicates its application.The theory and example of the proposed method show that the generalized quadratic form method take advantage of matrix characteristics,and is available in many cases.