Formal power series and input-output linearization of nonlinear discrete-time systems

After a summary of the results until now available, it is shown that the problem of the linearization by feed-back of the input-output behaviour of a given nonlinear system can be posed and solved by means of the "conversion" (inversion with respect to composition) of a formal power series. This brings to assume polynomial (in the input) analytic (in the state) feedback control laws and generalizes the previous results.