An elementary operation approach to the realization of multidimensional systems in Fornasini-Marchesini state-space model: The SISO case

This paper presents an elementary operation approach to the realization of single-input and single-output (SISO) multidimensional (n-D) systems in Fornasini-Marchesini (F-M) local state-space model. Specifically, the n-D realization problem is first formulated as an elementary operation problem of a certain n-D polynomial matrix. Then, a general constructive realization procedure will be proposed, which can generate an F-M model realization with lower order than the existing methods. A non-trivial example will be given to illustrate some details and the effectiveness of the proposed approach.