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Geometric techniques for implicit two-dimensional systems

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Abstract

Geometric tools are developed for two-dimensional (2-D) models in an implicit Fornasini–Marchesini form. In particular, the structural properties of controlled and conditioned invariance are defined and studied. These properties are investigated in terms of quarter-plane causal solutions of the implicit model given compatible boundary conditions. The definitions of controlled and conditioned invariance introduced, along with the corresponding output-nulling and input-containing subspaces, are shown to be richer than the one-dimensional counterparts. The analysis carried out in this paper establishes necessary and sufficient conditions for the solvability of 2-D disturbance decoupling problems and unknown-input observation problems. The conditions obtained are expressed in terms of output-nulling and input-containing subspaces, which can be computed recursively in a finite number of steps.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia

    Lorenzo Ntogramatzidis

  2. Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC, 3010, Australia

    Michael Cantoni

Authors
  1. Lorenzo Ntogramatzidis
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  2. Michael Cantoni
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Correspondence to Lorenzo Ntogramatzidis.

Additional information

This work was partially supported by the Australian Research Council (DP0986577 and FT12010060).

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Ntogramatzidis, L., Cantoni, M. Geometric techniques for implicit two-dimensional systems. Multidim Syst Sign Process 24, 601–620 (2013). https://doi.org/10.1007/s11045-012-0205-4

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  • DOI: https://doi.org/10.1007/s11045-012-0205-4

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