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The minimal realization problem in the max-plus algebra

  • Geert Jan Olsder
  • Bart De Schutter
Part of the Communications and Control Engineering book series (CCE)

Abstract

Given an arbitrary real sequence \(\left\{ {{g_i}} \right\}_{i = 1}^\infty \) elegant necessary and sufficiency conditions are known for the existence of an n × n matrix A, an n × 1 vector b and a 1 × n vector c, for some appropriate n, such that
$${g_i} = c{A^{i - 1}}b\,for i = 1,2, \ldots $$
(32.1)

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Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Geert Jan Olsder
    • 1
  • Bart De Schutter
    • 2
  1. 1.Department of Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands
  2. 2.ESAT-SISTAK. U. LeuvenLeuvenBelgium

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