Realization of multidimensional systems in Fornasini-Marchesini state-space model

This paper presents a constructive procedure that can generate a Fornasini-Marchesini (local) state-space model realization for a given n-D system with lower order than the existing procedure given by Alpay and Dubi. It is clarified that the method of Alpay and Dubi usually generates a realization with unnecessarily high order even for a simple rational transfer function, and, by taking into account of the structural characteristic of the given transfer function or transfer matrix, it is possible to construct a realization with much lower order. Nontrivial examples are given to illustrate the basic idea as well as the effectiveness of the proposed approach.