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

INRIA Sophia Antipolis, B.P. 93, 06902 Sophia Antipolis cedex, France; David.Avanessoff@sophia.inria.fr; Jean-Baptiste.Pomet@sophia.inria.fr

Received: 21 April 2005
Revised: 30 November 2005

Abstract

This paper studies Monge parameterization, or differential flatness, of control-affine systems 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.