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Effective algorithms for parametrizing linear control systems over Ore algebras

Applicable Algebra in Engineering, Communication and Computing volume 16, pages 319–376 (2005)Cite this article

Abstract

In this paper, we study linear control systems over Ore algebras. Within this mathematical framework, we can simultaneously deal with different classes of linear control systems such as time-varying systems of ordinary differential equations (ODEs), differential time-delay systems, underdetermined systems of partial differential equations (PDEs), multidimensional discrete systems, multidimensional convolutional codes, etc. We give effective algorithms which check whether or not a linear control system over some Ore algebra is controllable, parametrizable, flat or π-free.

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Authors and Affiliations

  1. INRIA Rocquencourt, ALGO project, Domaine de Voluceau BP 105, 78153, Le Chesnay Cedex, France

    F. Chyzak

  2. INRIA Sophia Antipolis, CAFE project, 2004, Route des Lucioles BP 93, 06902, Sophia Antipolis Cedex, France

    A. Quadrat

  3. Lehrstuhl B für Mathematik, RWTH – Aachen, Templergraben 64, 52056, Aachen, Germany

    D. Robertz

Authors
  1. F. Chyzak
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  2. A. Quadrat
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  3. D. Robertz
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Corresponding author

Correspondence to A. Quadrat.

Additional information

This paper is dedicated to the memory of our dear friend and colleague Manuel Bronstein.

The third author has been financially supported by the Control Training Site grant HPMT-CT-2001-00278 and the Deutsche Forschungsgemeinschaft during his stays at INRIA Sophia Antipolis.

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Chyzak, F., Quadrat, A. & Robertz, D. Effective algorithms for parametrizing linear control systems over Ore algebras. AAECC 16, 319–376 (2005). https://doi.org/10.1007/s00200-005-0188-6

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  • DOI: https://doi.org/10.1007/s00200-005-0188-6

Keywords

  • Linear systems over Ore algebras
  • Parametrization
  • Flatness
  • Constructive algorithms
  • Non-commutative Gröbner bases
  • Module theory

Mathematics Subject Classification (2000)

  • 93C05
  • 93B25
  • 16E30
  • 68W30
  • 13P10