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The transfer function of a full-order compensator for a single-input, single-output (SISO) linear system designed by the separation principle is uniquely determined by the locations of the poles of the closed-loop system and its gain. Hence, the poles of the observer and of the full-state feedback design can be interchanged without altering the transfer function of the compensator. A state space derivation of this property is presented.

A circuit realization is presented for generalized one-multiplier lattice discrete two-dimensional (2-D) filters. The proposed structure has a minimun mumber of delay elements and multipliers. Based on this circuit realization, the corresponding state-space realization-representation is derived. The dimension of the 2-D state-space vector is minimal and the corresponding transfer function is characterized by the all-pass property. Index Terms--State-space realization, two-dimensional filters, two dimensions.

In this paper, the discrete Fourier transform is used to determine the coefficients of a transfer function of a new generalized two-dimensional system of second-order: Ex(i1 + 2, i2 + 2) = A0x(i1 + 1, i2 + 1) + A1x(i1 + 1, i2) + A2x(i1, i2 + 1). The algorithm is straightforward and has been implemented using the software package Matlab™. A step-by-step example illustrating the application of the algorithm is presented. [ABSTRACT FROM AUTHOR]