Note on the Characteristic Polynomial Assignment Problem for 2-D Systems

In this paper, the problem of the characteristic polynomial assignment (CPA) for linear shift invariant single-input single-output (SISO) two-dimensional (2-D) systems is considered. Specifically, it is shown that the use of the Fornasini-Marchesini canonical state space model representation facilitates the determination of a feedback control law for assigning a 2-D characteristic polynomial, and always results in a solution to the CPA problem. As for the proof, the well known Bass-Gura method is used. The simplicity and efficiency of the method is illustrated by several examples

Generalized Two Dimensional Systems. Leverrier-Faddeeva Algorithm

A method for the transfer function computation of a generalized (singular) two-dimensional (2-D) state space model has been presented. The method is based on the Leverrier-Faddeeva algorithm for regular systems. The simplicity of the method is illustrated by an example

On a Property of Compensators Designed by the Separation Principle

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

Two-Dimensional Modified Cauer Form: Circuit and State Space Realisation

A new two-dimensional (2-D) continued fraction expansion, based on the modified Cauer form, has been formulated. Moreover, a minimal state space model realisation has been derived, based on its signal flow graph, using the proposed 2-D continued fraction expansion

Minimal Circuit and State Space Realization of Three-Term Separable Denominator 2-D Filters

A simple method is presented for the minimal state space realization of two dimensional (2-D) filters, with a three-term separable denominator (3TSD) made up of two 1-D and one 2-D terms. The matrix A and the vectors b and c of the state space model are derived explicitly from the coefficients of the initial transfer function. The circuit implementation for the 2-D 3TSD filters is provided, as well. The number of delay elements employed represents a significant reduction compared to earlier non-minimal realizations

Determination of Transfer Function of Two Dimensional Generalised Systems using the Discrete Fourier Transform

A systematic and conceptually simple algorithm is presented for the determination of the transfer function for two-dimensional generalised or singular systems. The method uses the discrete Fourier transform (DFT) and can easily be applied. The simplicity and efficiency of the algorithm are illustrated by two examples

Realization of Separable Nth Order 2D All-Pass Digital Filters

The realization, circuit and state space of two-dimensional (2D) nth order separable all-pass digital filters is considered. The matrices A, b, c′ and the scalar d of the Givone-Roesser state space model are presented in closed form. The dimension of the state space model is minimal. In addition, the corresponding circuit implementation of the filter is given

Two-Dimensional Systems; A Simple Proof of the Cayley-Hamilton Theorem

A simple proof of the Cayley-Hamilton theorem for the case of two-dimensional systems is presented. The proof is based on the recursive two-dimensional Leverrier-Faddeeva algorithm

Design of a Periodic Feedback Control Law for Systems with Higher Dimension

The problem considered in this paper is the design of a feedback control law such that the closed loop system meets desired performance specifications. Particularly, we are dealing with the exact model matching problem for systems with two-dimensions using periodic state and output feedback, assuming that the states and the output are accessible to measurements, and that noise is not present. The method leads to necessary conditions for the solution of the problem. To illustrate the procedure, two step-by-stem examples are presented

Determination of the Transfer Matrix of Multidimensional-Singular Systems

A computationally simple algorithm for determining the transfer function of multidimensional singular systems, described by a state-space model based on the Givone-Roesser state space setting, is proposed. The method uses the discrete Fourier transform and can be readily implemented on a digital computer. An example is given to illustrate the simplicity and the efficiency of the algorithm