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

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Analysis and Optimization of Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((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.

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References

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600, AJ, Delft, The Netherlands

    Geert Jan Olsder

Authors
  1. Geert Jan Olsder
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Editors and Affiliations

  1. Institut National de Recherche en Informatique et en Automatique, INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153, Le Chesnay, France

    A. Bensoussan  & J. L. Lions  & 

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© 1986 Springer Science+Business Media Dordrecht

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Olsder, G.J. (1986). On the Characteristic Equation and Minimal Realizations for Discrete-Event Dynamic Systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007557

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  • DOI: https://doi.org/10.1007/BFb0007557

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16729-7

  • Online ISBN: 978-3-540-39856-1

  • eBook Packages: Springer Book Archive

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