Abstract
Two-dimensional state-space systems arise in applications such as image processing, iterative circuits, seismic data processing, or more generally systems described by partial differential equations. In this paper, a new direct method is presented for the polynomial realization of a class of noncausal 2D transfer functions. It is shown that the resulting realization is both controllable and observable.
Highlights
A 2D system is a system in which information propagates in two independent directions
Rosenbrock [2] has used polynomial matrices in a single variable to represent systems described by ordinary differential/difference equations. The success of his approach is mainly due to the computational aspects of the division ring involved
In the case when two polynomial matrix description (PMD) P(s, z) and Q(s, z) are in statespace form (8) and have the same dimensions, we introduce the following notion of restricted-system equivalence (RSE)
Summary
A 2D system is a system in which information propagates in two independent directions. Multidimensional (nD) systems have found many applications in areas such as image and video processing, geophysical exploration, linear multipass processes, iterative learning control systems, lumped and distributed networks [1]. In his pioneering work, Rosenbrock [2] has used polynomial matrices in a single variable to represent systems described by ordinary differential/difference equations. Rosenbrock [2] has used polynomial matrices in a single variable to represent systems described by ordinary differential/difference equations The success of his approach is mainly due to the computational aspects of the division ring involved. The polynomial ring in two variables is not an Euclidean division ring which makes extensions from 1D to 2D in most situations not possible
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