Remarks on a Triangular Form for 1-Flat Pfaffian Systems with Two Inputs

We consider 1-flat nonlinear control systems with two inputs and a given 1-flat output. The control systems are represented as Pfaffian systems. It is well-known that flat systems can be transformed to Brunovsky normal form after applying an endogenous dynamic feedback, and only for static feedback linearizable systems this transformation is possible without dynamic feedback. However, there exists a normal form, denoted as implicit triangular form, which is a generalization of the Brunovsky normal form, and even systems which are not static feedback linearizable might possibly be transformed to this normal form without applying a dynamic feedback. Given a two-input nonlinear control system and a fixed 1-flat output, we provide necessary and suficient conditions to check whether such a transformation exists. Furthermore, we provide an algorithm to find this transformation.