A rigorous and detailed construction of the differential field K/sub Sigma /(u,y) associated, in a differential-algebraic context, to a nonlinear system Sigma described in state-space form with analytic coefficients is presented. The field K/sub Sigma /(u,y) represents an input-output description of Sigma , and its study is of key importance in problems concerning the input-output behavior of Sigma . Technically, the basic step of the construction of K/sub Sigma /(u,y) consists in proving that the differential ideal associated to the state-evolution equation of Sigma is prime.>
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Conte et al. (1993) studied this question.
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