Two-input control-affine systems linearizable via one-fold prolongation and their flatness

We study flatness of two-input control-affine systems, defined on an n-dimensional state-space. We give a complete geometric characterization of systems that become static feedback linearizable after a one-fold prolongation of a suitably chosen control. They form a particular class of flat systems: they are of differential weight n + 3. We give normal forms compatible with the minimal flat outputs and provide a system of first order PDE׳s to be solved in order to find all minimal flat outputs. We illustrate our results by two examples: the induction motor and the polymerization reactor.