Abstract
We give a characterization of differentially flat nonlinear systems in implicit representation, where the input variables are eliminated. Lie-Bäcklund isomorphisms associated to a flat system, called trivializations, can be locally characterized in terms of matrices polynomial with respect to d/dt. Such polynomial matrices are useful to compute the ideal of differential forms generated by the differentials of all possible trivializations. We introduce the notion of a strongly closed ideal of differential forms, and prove that flatness is equivalent to the strong closedness of the latter ideal.
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