状态方程约当化的一种方法

本文根据系统特征方程的特征值和特征值所对应的特征向量数目的不同情况,首先直接构造系数矩阵A的相似约当阵,然后利用变换关系式求非奇异变换阵Q,以使状态方程变换成约当(或对角)标准形。该法避免了通常约当化时必须计算特征向量,特别是广义特征向量的繁琐过程,从而使状态空间表达式约当化问题简单易行。

A METHOD OF STATE EQUATION JORDAN TRANSFORMATION

This paper first on the basis of different conditions of system characteristic equation eigenvalues and the eigenvcctor numbers associated with the eigen values directly forms sim- ilarity Jordan matrix of the coefficient matrix A. Then this paper makes use of transforma- tion of relational exprcssion to find the nonsigular trasformation matrix Q in order to transform the state equations to Jordan (or: diagonal) canonical form. This method avoids too complicated proccdure which must compute eigenvalues, es- pecially generalized eigenvalucs in detail, so it makes the state space representative equa- tion transform Jordan problem more simple.