Abstract
For nonlinear systems described by algebraic differential equations (in terms of “state” or “latent” variables) we examine the converse to realization,elimination, which consists of deriving an externally equivalent representation not containing the state variables. The elimination in general yields not only differential equations but also differentialinequations. We show that the application of differential algebraic elimination theory (which goes back to J.F. Ritt and A. Seidenberg) leads to aneffective method for deriving the equivalent representation. Examples calculated by a computer algebra program are shown.
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This paper was written while the author was with the Systems Division of the Laboratoire des Signaux et Systèmes in Gif-Sur-Yvette and was supported by the University of Orléans, France.
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Diop, S. Elimination in control theory. Math. Control Signal Systems 4, 17–32 (1991). https://doi.org/10.1007/BF02551378
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DOI: https://doi.org/10.1007/BF02551378