A sufficient condition for full linearization via dynamic state feedback

The purpose of this paper is to show that any square invertible nonlinear system whose inverse is "state-free" can be turned into a fully linear controllable and observable system by means of dynamic state-feedback and coordinates transformations. A nonlinear system has an inverse which is "state-free" if the value of the input (at time t) can be expressed as a function of the values (at t) of the output and a finite number of its derivatives.