用SVD求矩阵广义特征向量以求状态方程解析解

本文讨论了一种直接在时域范围内求解线性时不变网络的状态方程（Ｘ＝ＡＸ）解析解的一种方法。当系数矩阵Ａ的特征值出现重根时利用奇异值分解的方法求广义特征向量然后求解。对非齐次状态方程（ＸＡＸＢＵ）首先用扩展状态空间的方法把它化为齐次方程。

THE ANALYTIC SOLUTION OF STATE EQUATIONS BY USING SVD

This paper gives a computational algoritnm, by which analytic solution of the state equation(X=AX+BU )is given directly in time-domain. The key tool of its success is SVD. No matter whether the eigenvalues of the transi- tion matrix A are distinct or not, this algorithm will be always successful.