State-space models of 3-D transfer function matrix

Abstract

An algorithm for obtaining two different state-space models of all three-dimensional (3-D) transfer function matrices is given. The resulting 3-D models are the 3-D analogue of the Roesser 2-D model and Eising 2-D model. The relation between these two models is also given. The approach is based on the construction of the Hankel matrix from the polynomial coefficients of a negative power series expansion of 3-D, 2-D, and 1-D transfer function matrices, respectively. The proposed algorithm results in a few large system matrices for the 3-D model analogue of the Roesser 2-D model, while there are more system matrices for the 3-D model analogue of the Eising 2-D model but of a smaller order.