A novel constructive procedure to low-order Fornasini–Marchesini model realization

Abstract

In this paper, a novel constructive procedure is proposed for the realization of a low-order Fornasini–Marchesini state-space model for a given multidimensional system. In particular, essential properties for the constructions of a backward shift space and a resolvent invariant space associated with the Gleason’s problem from a given transfer function matrix are investigated and some new sufficient conditions for such constructions are developed. Then, based on these conditions, a systematic constructive procedure is proposed for the multidimensional Fornasini–Marchesini model realization. It turns out that the new constructive procedure can generate Fornasini–Marchesini models with much lower orders and even the minimal realizations for a much larger class of multidimensional systems than the existing methods. Nontrivial examples are also provided to illustrate the basic idea as well as the effectiveness of the proposed procedure.