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A generalized controller canonical form for linear and nonlinear dynamics is proposed. It is obtained using the theorem of the primitive element from differential algebra. The derivation of the controller form does not apply to multivariable constant linear systems. With the transformations, all nonlinear dynamics can be exactly linearized by dynamic feedback. The main departure from standard theory is that transformations may depend on input derivatives. Once differential-algebraic tools are introduced, the proofs of the results are easy.>
Michel Fliess (Mon,) studied this question.