Realizations of Polynomial Systems

  • Zbigniew Bartosiewicz
Part of the Mathematics and Its Applications book series (MAIA, volume 29)


This paper is a continuation of the previous author s paper [1], where a new definition of a polynomial input-output system has been proposed. We have been interested in immersions of nonlinear systems into polynomial ones (immersions into simpler systems as affine or linear ones have been studied by Fliess and Kupka [4], Claude, Pliess and Isidori [2] and Claude [3]. The observation algebra of a nonlinear system has appeared to be a useful tool for examination of this problem. Finite generatedness and regularity of the observation algebra are necessary and sufficient in order that the nonlinear system may be regularly immersed into an algebraically observable polynomial system. Here we study a more general case — without assumptions about regularity and observability. Now the observation algebra does not have to be finitely generated but has to be a subalgebra of a finitely generated algebra. However, we complete the result of [1] proving that if the observation algebra is finitely generated then there is an immersion into an algebraically observable polynomial system.


Nonlinear System Polynomial System Ring Homomorphism Polynomial Realization Minimal Realization 
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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Zbigniew Bartosiewicz
    • 1
  1. 1.Instytut MatematykiPolitechnika BiałostockaBiałystokPoland

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