The solution of the matrix polynomial equation<tex>A(s)X(s) + B(s)Y(s) = C(s)</tex>

Abstract

This note presents an algorithm for finding the solution <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{X(s), Y(s)\}</tex> of the matrix polynomial equation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A(s)X(s) + B(s)Y(s) = C(s)</tex> . Since the solution, when it exists, is not unique we will find the solution for which the rows of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X(s)</tex> have a minimal possible degree. This procedure will result in a unique solution that is obtained by solving a set of linear equations. An example is given to illustrate the procedure.