A non-exact Brunovsky form and dynamic feedback linearization

A procedure is given to describe any nonlinear control system in a so-called nonexact Brunovsky form. A system is shown to be differentially flat, a property which is sufficient to be linearizable by dynamic feedback, if, and only if, the basis of this Brunovsky form can be represented as an equivalent system of exact one-forms. Sufficient conditions for equivalence between a basis of the Brunovsky form and a system of exact one-forms are given in the case of two-input systems. These sufficient conditions lead to a constructive procedure.<>