New algorithms for the derivation of the transfer-function matrices of 2-D state-space discrete systems

New algorithms for the derivation of the transfer-function matrices of two-dimensional (2-D) discrete systems from the Roesser and Fornasini-Marchesini state-space models are presented. Two key steps in developing the algorithms are as follows. First, the transfer-function matrix is reformulated in terms of the characteristic polynomials of the matrices involved. Second, an efficient algorithm for the determination of 1-D polynomial coefficients is developed and is, in turn, used to determine the coefficient matrices of the 2-D transfer-function matrix. The proposed algorithms are computationally efficient and reliable. The efficiency of the algorithms is illustrated by comparing the proposed method with two existing methods through examples.