Lyapunov矩阵方程式的解析解

An Explicit Solution of the Lyapunov Matrix Equation

本文提出了一种Lyapunov矩阵方程的解析解法。运用此法,通过简单的标量计算降低了矩阵运算处理的阶数,而且在方程唯一解存在的情况下,对已知矩阵不加任何条件限制,也不用施行任何矩阵变换运算,就可求得其解。

This paper proposed an explicit solution for the Lyapunov Matrix. The equation can be solved by N(N-1)/2 simultaneous linear equations without any restricts to and transformation operations on the given matrixes. A numerical example is considered to illustrate the mathod of solution.