ABSTRACT
In this chapter we present some controller design examples related to multivariable nonlinear systems which exhibit the flatness property. While there is no general methodology for assessing the flatness of a multivariable nonlinear system, specially in those cases where a dynamic extension of the system is necessary to render it linearizable by means of static state feedback and change of coordinates, the presented examples depict the simplicity associated with feedback controller design in multivariable systems which happen to be flat. Flatness also offers a clue on how to suitably extend the nonlinear system in order to obtain a “matched” relation between the control inputs and the higher order derivatives of the several flat outputs from where invertibility can be assessed. Evidently, we do not have any general guarantee that suitable extensions of the original system always result in an invertible input-to-flat output higher order derivative map.
