A new method for solving Bezout equations over 2-D polynomial matrices from delay systems

In the algebraic system theory of delay systems, it is well known that under spectral controllability or canonicity, a Bezout equation set up with a coprime pair of 2-D polynomial matrices has a solution in polynomial matrices with coefficient belonging to a ring of entire functions. We propose a new method for solving such Bezout equations. The basic concept involves the reduction of a Bezout equation over 2-D polynomial matrices to a simple scalar equation over 1-D polynomials. Due to the basic concept, it can be used to calculate a solution even by hand and is particularly efficient in the absence of modern computer algebra systems.