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On the Characteristic Equation and Minimal Realizations for Discrete-Event Dynamic Systems

  • Geert Jan Olsder
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)

Abstract

Recently an analogy between conventional linear system theory and the relatively new theory on discrete-event dynamic systems has been shown to exist. The system descrip-tion in the new theory resembles the one of the conventional theory, provided that the operations addition and multiplication are replaced by maximization and addition respectively. One also speaks of a system in the max-algebra, which is a semi-ring. In this paper we investigate, by pursuing the analogy mentioned above, whether mini-mal realizations exist for discrete-event dynamic system if only the input/output description is given by means of the impulse response. A constuction procedure is suggested. It turns out that the characteristic equation of a matrix in the max-al-gebra (to be defined) plays a crucial rôle.

Keywords

Impulse Response Characteristic Equation Characteristic Polynomial Realization Theory Conventional Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • Geert Jan Olsder
    • 1
  1. 1.Dept. of Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands

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