Sylvester矩阵方程组特殊解的H-表示解法

H-Representation Method for Special Solutions of Sylvester Matrix Equations

利用矩阵的H-表示方法研究Sylvester矩阵方程组的Hankel解和Toeplitz解。根据Hankel矩阵和Toeplitz矩阵的结构特点,利用H-表示将矩阵方程组转化为向量值方程,进而给出矩阵方程组在Hankel及Toeplitz约束下相容的充要条件及通解表达式,通过数值算例,说明H-表示方法的有效性和优越性。最后给出利用本文方法求解特殊时不变耦合矩阵方程Toeplitz解的例子。

Using the H-representation of matrix,we study the Hankel solution and Toeplitz solution of Sylvester matrix equations.According to the structural characteristics of Hankel matrix and Toeplitz matrix,the matrix equations are transformed into vector-valued equation by using H-representation,and then the necessary and sufficient conditions for the compatibility of matrix equations under Hankel and Toeplitz constraints and the general solutions expression are given.Numerical examples show the effectiveness and superiority of H-representation method.Finally,an example for solving Toeplitz solution of special time-invariant coupled matrix equations by using the method proposed in the paper is given.