Time-domain description of behaviors over finite fields

R. van de Kreeke, Jan W. Polderman

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    We consider autonomous behaviors over a finite field with characteristic values that do not necessarily belong to the field. The time domain description of the behavior is given in a suitable field extension of the base field. The problem that we consider is how to derive a description completely within the base field. For the case of behaviors over the reals there is a common splitting field for all irreducible polynomials, the complex field. Complex trajectories induce real trajectories by restricting coefficients of complex conjugate exponentials to be complex conjugate as well. For the case of finite fields the situation is more complicated as there does not exist a single finite field extension in which all polynomials over the base field split. In this paper we describe a systematic procedure to obtain explicit expressions for all trajectories in the behavior whose components take values in the base field.
    Original languageUndefined
    Title of host publicationProceedings of the 18th International symposium on Mathematical Theory of Networks and Systems
    Place of PublicationBlacksburg
    PublisherVirginia Tech
    Number of pages12
    ISBN (Print)not assigned
    Publication statusPublished - Jul 2008
    Event18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008 - Blacksburg, United States
    Duration: 28 Jul 20081 Aug 2008
    Conference number: 18

    Publication series

    PublisherVirginia Tech


    Conference18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008
    Abbreviated titleMTNS
    CountryUnited States


    • EWI-15327
    • IR-65482
    • METIS-263836

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