Output Dependent Observability Linear Normal Form

This paper gives the sufficient and necessary conditions which guarantee the existence of a diffeomorphism and an output injection in order to transform a nonlinear system in a ‘canonical’ normal form depending on its output. We propose two methods: one is based on the commutativity via the Lie brackets of a family of vector fields and the second one is the dual of the first one, based on the closure of a family of 1-forms.