The analytical general solutions to the higher-order Sylvester matrices equation
高阶Sylvester矩阵方程的解析通解

Three completely analytical parametric solutions to the matrices equation A_{m1}V J^{m1} +...+A_1V J +A_0V = B_{m2}WJ^{m2} +...+B_1WJ +B_0W 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.