Effective algorithms for parametrizing linear control systems over Ore algebras

Article

DOI: 10.1007/s00200-005-0188-6

Cite this article as:
Chyzak, F., Quadrat, A. & Robertz, D. AAECC (2005) 16: 319. doi:10.1007/s00200-005-0188-6

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.

Keywords

Linear systems over Ore algebrasParametrizationFlatnessConstructive algorithmsNon-commutative Gröbner basesModule theory

Mathematics Subject Classification (2000)

93C0593B2516E3068W3013P10

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.INRIA Rocquencourt, ALGO projectLe Chesnay CedexFrance
  2. 2.INRIA Sophia Antipolis, CAFE projectSophia Antipolis CedexFrance
  3. 3.Lehrstuhl B für Mathematik, RWTH – AachenAachenGermany