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

Abstract. This paper studies Monge parameterization, or differential flatness, of control-affine sys-tems with four states and two controls. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about “(x, u)-flatness ” of these systems, with much more elementary techniques