Orthogonality Measures and Applications in Systems Theory in One and More Variables

  • Adhemar Bultheel
  • Annie Cuyt
  • Brigitte Verdonk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)


The representation or order reduction of a rational transfer function by a linear combination of orthogonal rational functions offers several advantages, among which the possibility to work with prescribed poles and hence the guarantee of system stability. Also for multidimensional linear shift-invariant systems with infinite-extent impulse response, stability can be guaranteed a priori by the use of a multivariate Padé-type approximation technique, which is again a rational approximation technique. In both the one- and multidimensional case the choice of the moment functional with respect to which the orthogonality of the functions in use is imposed, plays a crucial role.


Transfer Function Impulse Response Orthogonal Polynomial Order Reduction Rational Approximant 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Adhemar Bultheel
    • 1
  • Annie Cuyt
    • 2
  • Brigitte Verdonk
    • 2
  1. 1.Dept of Computer ScienceKatholieke Universiteit LeuvenHeverleeBelgium
  2. 2.Dept of Mathematics and Computer ScienceUniversity of AntwerpAntwerpBelgium

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