Spectral decomposition based solutions to the matrix equation AX-XB=C
Spectral decomposition based solutions to the matrix equation AX-XB=C
复制标题
基于谱分解的矩阵方程 AX - XB = C 的解
DOI：
10.1049/iet-cta.2017.0729
复制
发表时间：
2018
影响因子：
2.6
通讯作者：
Zhou Bin
中科院分区：
文献类型：
--
作者：
Li Zhao-Yan;Zhou Bin
本文利用a和b的谱分解方法研究了在控制理论中有重要应用的矩阵方程。通过建立标准矢量方程的可解性条件和解，以及矩阵方程相关系数的谱分解，给出了矩阵方程可解性的充分必要条件。此外，还根据a和b的光谱分解系数给出了显式解。所得结果作为特例纳入了现有方法，并对现有方法中的一些错误进行了修正。通过算例验证了该方法的有效性。
This study studies the matrix equation , which has many important applications in control theory, by using spectral decompositions ofAandB. By establishing solvability conditions and solutions to the standard vector equation , and the spectral decompositions of the associated nivellateur of the matrix equation, necessary and sufficient conditions for the solvability of the matrix equation are provided in terms of the coefficients of the spectral decompositions ofAandB. Moreover, explicit solutions are provided, which are also based on the coefficients of the spectral decompositions ofAandB. The obtained results include the existing ones as special cases, and, moreover, correct some errors in the existing methods. The effectiveness of the proposed approach is demonstrated by some illustrative examples.