Determination of the transfer-function matrix from the two-dimensional Fornasini-Marchesini state-space model

Two efficient algorithms for the determination of the transfer-function matrix of a two-dimensional (2-D) discrete system represented by the Fornasini-Marchesini state-space model are proposed. The development of the algorithms involves two distinct steps. First, the 2-D transfer-function matrix is reformulated in terms of the characteristic polynomials of the coefficient matrices involved. Second, the coefficient matrices are determined by using an efficient algorithm for the determination of l-D polynomial coefficients. The simplicity and efficiency of the proposed algorithms are illustrate by examples