Normal forms for multi‐input flat systems of minimal differential weight

International audienceWe present normal forms for nonlinear control systems that are the closest to static feedback linearizable ones, that is, for systems that become feedback linearizable via the simplest dynamic feedback, which is the one‐fold prolongation of a suitably chosen control. They form a particular class of flat systems, namely those of differential weight n + m + 1, where n is the number of states and m is the number of controls. We also show that the dynamic feedback may create singularities in the control space depending on the state and we discuss them. We also address the issue of the normalization of the system only versus that of the system together with a flat output. Finally, we illustrate our results by several examples