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Elementary operation approach to state-space realizations of 2-D systems. (English) Zbl 0874.93028
Linear 2-D discrete systems with constant coefficients are considered. Using purely algebraic methods and special elementary operations over the ring of two-variable polynomials, algorithms for various state-space realizations of the Roesser-type two-variable transfer function are introduced and discussed. A similar elementary approach is then used to solve the state-space realization problem for 2-D Fornasini-Marchesini models. A simple illustrative numerical example is also given. Moreover, a deep discussion on the relationships between state-space models for various kinds of 2-D regular and singular systems is presented. Similar elementary operation methods for 2-D linear systems have been discussed in the paper [K. Gałkowski, Int. J. Control 63, No. 6, 1129-1148 (1996; Zbl 0851.93012)].

93B15 Realizations from input-output data
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
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