A procedure for n-D Fornasini-Marchesini state-space model realization based on right matrix fraction description

Abstract

Since the duality between an n-D transfer matrix and its transpose does not hold for the n-D Fornasini-Marchesini (F-M) (local) state-space model, the existing realization method based on a left matrix fraction description (MFD) is not applicable to an n-D system described by a right MFD. The purpose of this paper is to propose a new constructive procedure that can generate an F-M state-space model realization for an n-D system given by a right MFD. The effectiveness of the proposed procedure will be demonstrated by a numerical example.