In this paper, following ideas recently developed for a class of continuous systems, we introduce the notion of zero dynamics and minimum phase for discrete time nonlinear systems. On this basis, sufficient conditions are given for state feedback stabilization and full linearization via dynamic compensation. Relations with other properties of the system are also investigated.

The purpose of this work is to show the real need to motivate theoretical research in nonlinear digital control not only for solving control problems which are specific to the context, but also for giving the intuition of new control methodologies. Digital control methods can, indeed, be used either for the design of piecewice constant feedback strategies or for the design of discontinuous and hybrid controllers.

It is shown that the formalism of asymptotic series expansions recently developed by the authors for computing the solutions of non autonomous differential equations, can be profitably employed to obtain the equivalent model to a nonlinear continuous system under generalized sampling procedures. Tools and insights for the design of sampled-data control systems are derived.