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Elimination in control theory. (English) Zbl 0727.93025
Summary: 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 differential inequations. We show that the application of differential algebraic elimination theory (which goes back to J. F. Ritt and A. Seidenberg) leads to an effective method for deriving the equivalent representation. Examples calculated by a computer algebra program are shown.

MSC:
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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