矩阵方程AX-XB=C非奇异解的存在性

Existence of a Nonsingular Solution to the Matrix Equation AX-XB=C

本文讨论了矩阵方程AX-XB =C非奇异解的存在性问题 ,并给出了该方程非奇异解存在的几个充分条件 .同时 。

In this paper, the existence problem is discussed of a nonsingular solution to the matrix equation AX-XB=C, and several sufficient conditions are given for the existence of a nonsingular solution to it. In addition, simple formula is presented for constructing Lyapunov function in linear systems.