The solution of the matrix polynomial equation A(s)X(s) + B(s)Y(s) = C(s)
J. F. Feinstein, Yeheskel Bar-Ness · IEEE Transactions on Automatic Control · 1984
This note presents an algorithm for finding the solution\{X(s), Y(s)\}of the matrix polynomial equationA(s)X(s) + B(s)Y(s) = C(s). Since the solution, when it exists, is not unique we will find the solution for which the rows ofX(s)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.