Flatness of two-input control-affine systems linearizable via a two-fold prolongation

International audienceWe study flatness of two-input control-affine systems, defined on an n-dimensional state-space. We give a geometric characterization of systems that become static feedback linearizable after a two-fold prolongation of a suitably chosen control. They form a particular class of flat systems: they are of differential weight n + 4. We present a normal form compatible with the minimal flat outputs

Flatness of multi-input control-affine systems linearizable via one-fold prolongation

International audienceWe study flatness of multi-input control-affine systems. We give a geometric characterization of systems that become static feedback linearizable after an invertible one-fold prolongation of a suitably chosen control. They form a particular class of flat systems. Namely, they are of differential weight n + m + 1, where n is the dimension of the state-space and m is the number of controls. We propose conditions (verifiable by differentiation and algebraic operations) describing that class and provide a system of PDE's giving all minimal flat outputs. We illustrate our results by an example of the quadrotor helicopter

A Structurally Flat Triangular Form Based on the Extended Chained Form

In this paper, we present a structurally flat triangular form which is based on the extended chained form. We provide a complete geometric characterization of the proposed triangular form in terms of necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to this triangular form. This yields a sufficient condition for an affine input system to be flat.Comment: arXiv admin note: substantial text overlap with arXiv:2002.0120