运动稳定性的一种判定方法

A METHOD FOR DETERMINING THE STABILITY OF MOTION

根据矩阵相似变换理论将给定系统的系数矩阵Ａ＝［ａ＿（ｉｊ）］ｎ×ｎ简化为上Ｈｅｓｓｅｎｂｅｒｇ型，通过寻求简化后的判定阵Ｄ＝［ｄ＿（ｉｊ）］来判定原系统Ａ的稳定性。由于这种方法不需要求出系统系数矩阵的特征方程或特征根，给大系统分析带来一些方便。

method for determining the stability of dynamic system is discussed in this paper.In the method the coefficient matrix of the differential equations of dynamical system A=(a_(ij))n×n is transformed to upper Hessenberg fonn by similarity transformation. Based on the diagonal matrix D=[d_(ij)] obtained by interative procedures of change parameters,the stability of origi-nal system A is determined.The characteristic equations or eigenvalues of the matrix A need not be calculated by this method,it is convenient to detennine the stability of large scale system.The application of the method is illustrated by an example.