On the minimal state-space realizations of all-pole and all-zero 2-D systems

A simple method is presented for the minimal state-space representation, described by the Roesser model, of a 2-D all-pole and all-zero transfer function. The state-space representation is derived, from a block diagram, by inspection. General expressions for the system matrices of very simple form are derived explicitely in terms of the parameters of the transfer function.