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

e study the problem to provide an implicit triangular form for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method, how to transform a given system into that special triangular shape, if possible. The well known Brunovsky form, which is applicable with regard to the input to state linearization problem, can be seen as special case of this implicit triangular form. A key tool in our investigation will be the construction of certain Cauchy characteristic vector fields that additionally annihilate certain distributions, and that will correspond to variables whose time-evolution can be derived without any integration