On Equivalence and Feedback Equivalence to Finitely Computable Sampled Models

The paper deals with the finiteness of the series expansions representing the sampled model of a nonlinear plant after coordinates transformation and state feedback. Such a property makes the computation of the exact sampled model possible by finite calculations: "finite computability". Necessary and sufficient conditions are given for the class of controllable driftless dynamics. Some constructive approaches to the computation of the solutions are discussed. The results are extended to the class of underactuated mechanical systems.