On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input uu and state xx. A given set of functions vv, which is not necessarily the original input uu of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input vv. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems.