Parametric Solutions to the Generalized Discrete Yakubovich-Transpose Matrix Equation.

This paper is concerned with the complete parametric solutions to the generalized discrete Yakubovich-transpose matrix equation X − AX^TB = CY. which is related with several types of matrix equations in control theory. One of the parametric solutions has a neat and elegant form in terms of the Krylov matrix, a block Hankel matrix and an observability matrix. In addition, the special case of the generalized discrete Yakubovich-transpose matrix equation, which is called the Karm- Yakubovich-transpose matrix equation, is considered. The explicit solutions to the Karm- Yakubovich-transpose matrix equation are also presented by the so-called generalized Leverrier algorithm. At the end of the paper, two examples are given to show the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]