Elsevier

Automatica

Volume 28, Issue 2, March 1992, Pages 345-354
Automatica

Paper
A review of 2-D implicit systems,☆☆

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Abstract

The one-dimensional notion of causality has no counterpart in the two-dimensional plane, where at best partial orderings of (i, j) may be defined. Two-dimensional implicit systems, unlike the familiar state-space 2-D models, do not require any notion of causality or recursibility. Instead, they require the milder notion of regularity. Thus, the implicit models are more suited to the description of naturally occurring two-dimensional systems, such as are described by the hyperbolic equation and the heat equation, as well as for applications in image processing. This paper provides a brief summary of the current state of the theory of 2-D implicit systems.

References (14)

  • W. Marszalek

    Two-dimensional state-space discrete models for hyperbolic partial differential equations

    Appl. Math. Modelling

    (1984)
  • N.K. Bose

    Applied Multidimensional Systems Theory

    (1982)
  • G. Conte et al.

    A geometric approach to the theory of 2-D systems

    IEEE Trans. Aut. Control

    (1988)
  • E. Fornasini et al.

    Doubly indexed dynamical systems: state-space models and structural properties

    Math. Systems Theory

    (1970)
  • T. Kaczorek

    Two-Dimensional Linear Systems

    (1985)
  • S.-Y. Kung et al.

    New results in 2-D systems theory, Part II: 2-D state-space models—realization and the notions of controllability, observability, and minimality

There are more references available in the full text version of this article.

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The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor V. Kučera under the direction of Editor H. Kwakernaak.

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Research supported by NSF Grant ECS-8805932.

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