Determination of transfer function of two dimensional generalised systems using the discrete Fourier transform

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

“…From these examples, it is evident that both Algorithms 1 and 2 lead to a significant reduction in the amount of computation relative to the Fadeeva and DFT Algorithms [19], [22]. The DFT algorithm, which exploits the efficiency of the fast Fourier transform (FFT), is efficient for high-order systems; nevertheless, our algorithms are more efficient.…”

“…In Section IV-A, Algorithms 1 and 2 are applied to four 2-D discrete systems represented by the Roesser state-space model and the required amounts of computation are compared with those required by the existing algorithms [19], [22]. In Section IV-B, Algorithms 3 and 4 are applied to two systems represented by the Fornasini-Marchesini state-space model.…”

“…The transfer-function matrix obtained by using Algorithms 1 and 2, and the Algorithms in [19] and [22] is where the denominator is given by the matrix: and the numerators are specified by , , , and as follows: e14…”

“…The system is represented by the Roesser state-space model with the matrices: Algorithms 1 and 2 proposed and the algorithms in [19] and [22] led to the transfer function where The amounts of computation required by the various algorithms are listed in Table I. Example 2 is a two-input two-output system represented by the Roesser model of order (2, 2), which was used to illustrate the algorithm in [19]. The model is given by (19a) and (19b) with…”

“…Several algorithms for the derivation of the 2-D transfer-function matrix from the Roesser state-space model have been proposed [17]- [22]. Those in [17]- [19] are basically extensions of the well-known Fadeeva algorithm [23] to the 2-D case while the algorithms in [20]- [22] are based on the discrete Fourier transform (DFT). Another popular state-space representation for 2-D discrete systems is the Fornasini-Marchesini model [24].…”