A New Solution to the Matrix Equation X−AX¯B=C

Abstract EN

We investigate the matrix equation X−AX¯B=C.

For convenience, the matrix equation X−AX¯B=C is named as Kalman-Yakubovich-conjugate matrix equation.

The explicitsolution is constructed when the above matrix equation has unique solution.

And this solution isstated as a polynomial of coefficient matrices of the matrix equation.

Moreover, the explicit solutionis also expressed by the symmetric operator matrix, controllability matrix, and observability matrix.

The proposed approach does not require the coefficient matrices to be in arbitrary canonical form.

At the end of this paper, the numerical example is shown to illustrate the effectiveness of theproposed method.