Nonlinear system approximations

We are interested in approximating a nonlinear system by a feedback linearizable system instead of a linear system. Two approaches presently exist in the literature. One involves the concept of involutivity to a certain order, and the other considers a canonical expansion and pure feedback approximation. We show the relationship between these two methods. This provides insight into lower order invariants in the equivalence problem for two nonlinear systems. Moreover, the output time responses for a nonlinear system and its feed-back linearizable approximation are mentioned.