On an implicit triangular decomposition of nonlinear control systems that are 1-flat—A constructive approach

In this paper we investigate a triangular form based on implicit differential equations for nonlinear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a given system into that special triangular shape, if possible. The well-known Brunovsky form, which is applicable with regard to the exact linearization problem, can be seen as a special case of this implicit triangular form. A key tool in our investigation will be the construction of Cauchy characteristic vector fields that additionally annihilate certain codistributions. In adapted coordinates this construction allows us to single out variables whose time-evolution can be derived without any integration.