Parametric Solutions to the Generalized Discrete Yakubovich‐Transpose Matrix Equation. Issue 4 (11th September 2013) - Song, Caiqin; Feng, Jun‐e; Wang, Xiaodong; Zhao, Jianli
Abstract This paper is concerned with the complete parametric solutions to the generalized discrete Yakubovich‐transpose matrix equation X − AXTB = 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.