STATE-SPACE REALIZATION OF 2-D FINITE-DIMENSIONAL BEHAVIORS

This paper deals with the state space realization of autonomous autore gressive two-dimensional (2-D) systems in the context of the behaviour al approach. An arbitrary autoregressive 2-D system Sigma can be viewe d as the sum of an externally controllable subsystem Sigma(c) with an autonomous one Sigma(a), so that a state space realization of Sigma ca n be obtained by separately realizing Sigma(c) and Sigma(a). Since a p rocedure for realizing externally controllable systems in state/drivin g-variable form is already available in the literature, the general re alization problem is easily reduced to the autonomous case. Here, some properties of finite-dimensional autonomous systems are discussed, al lowing for a realization procedure that uses the Grobner bases theory.