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.
|Title of host publication||Proceedings of the 18th International symposium on Mathematical Theory of Networks and Systems|
|Place of Publication||Blacksburg|
|Number of pages||12|
|ISBN (Print)||not assigned|
|Publication status||Published - Jul 2008|
|Event||18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008 - Blacksburg, United States|
Duration: 28 Jul 2008 → 1 Aug 2008
Conference number: 18
|Conference||18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008|
|Period||28/07/08 → 1/08/08|
van de Kreeke, R., & Polderman, J. W. (2008). Time-domain description of behaviors over finite fields. In Proceedings of the 18th International symposium on Mathematical Theory of Networks and Systems (pp. 059). Blacksburg: Virginia Tech.