高阶Sylvester矩阵方程的解析通解

The analytical general solutions to the higher-order Sylvester matrices equation

给出了矩阵方程Am1V Jm1+...+A1V J+A0V=Bm2WJm2+...+B1WJ+B0W的3种完全解析参数通解.这些解由一组参数向量给出,这些参数向量提供了问题的全部自由度.求解算法不要求矩阵J具有不同的特征值,或者和A(s)的特征值不同.这些通解仅包含数值矩阵计算,为工程应用计算提供了方便.算例说明本文所给方程通解的有效性.

Three completely analytical parametric solutions to the matrices equation Am1V Jm1＋...＋A1V J＋A0V = Bm2WJm2 ＋...＋ B1WJ ＋ B0W are presented.These solutions are expressed in terms of parameter vectors,which provide the design degrees of freedom.These approaches do not require the eigenvalues of J to be distinct or to be different from the roots of A（s）.Moreover,the obtained solutions contain only numerical matrix calculations,which provide convenience for the computation of these solutions in applications.A numerical example validates the proposed approaches.