Note on the characteristic polynomial assignment problem for 2-D systems

In this paper, the problem of the characteristic polynomial assignment (CPA) for linear shift invariant single-input single-output (SISO) two-dimensional (2-D) systems is considered. Specifically, it is shown that the use of the Fornasini-Marchesini canonical state space model representation facilitates the determination of a feedback control law for assigning a 2-D characteristic polynomial, and always results in a solution to the CPA problem. As for the proof, the well known Bass-Gura method is used. The simplicity and efficiency of the method is illustrated by several examples.