Abstract
Symbolic computation techniques are used to obtain a canonical form for polynomial matrices arising from discrete 2D linear state-space systems. The canonical form can be regarded as an extension of the companion form often encountered in the theory of 1D linear systems. Using previous results obtained by Boudellioua and Quadrat (2010) on the reduction by equivalence to Smith form, the exact connection between the original polynomial matrix and the reduced canonical form is set out. An example is given to illustrate the computational aspects involved.
Highlights
Canonical forms play an important role in the modern theory of linear systems
The so-called companion matrix has been used by many authors in the analysis and synthesis of 1D linear control systems
Barnett [1] showed that many of the concepts encountered in 1D linear systems theory such as controllability, observability, stability, and pole assignment can be nicely linked via the companion matrix
Summary
Canonical forms play an important role in the modern theory of linear systems. In particular, the so-called companion matrix has been used by many authors in the analysis and synthesis of 1D linear control systems. Boudellioua [2] suggested a matrix form which can be regarded as a 2D companion form for a class of bivariate polynomials. These polynomials arise in the study of 2D linear discrete state-space systems describing, for example, 2D image processing systems, as suggested by Roesser [3]. The author did not establish the exact connection between the original matrix and the reduced canonical form. In this paper, using symbolic computation based on the OreModules [4] Maple package the connection between the original polynomial matrix and the canonical form is established
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