Realization of a nonlinear system in the feedforward form: a polynomial approach

International audienceThe paper studies the problem of finding a realization of a nonlinear system described by a higher-order input-output differential equation in the so-called feedforward form. A necessary and su fficient condition for the problem to be solvable is given, and it is represented by the requirement that the corresponding polynomial description of the input-output equation can be factorized. Then certain one-forms associated to the factorization are always integrable which allows to write down the realization. The results are also applied to derive a necessary and su fficient condition for the transformation of a nonlinear state equation into the feedforward form