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A novel constructive procedure to low-order Fornasini-Marchesini model realization. (English) Zbl 1430.93037

Summary: 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.

MSC:

93B15 Realizations from input-output data
93B11 System structure simplification
93C55 Discrete-time control/observation systems
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
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