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This paper studies Monge parameterization, or differential flatness, ofcontrol-affine systems with four states and twocontrols. Some of them are knownto be flat, and this implies admitting a Monge parameterization. Focusing onsystems outside this class, we describe the only possible structure of such aparameterization for these systems, and give a lower bound on the order of thisparameterization, if it exists. This lower-bound is good enough to recover theknown results about "(x,u)-flatness" of these systems, with much moreelementary techniques.

Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states