Finitely discretizable nonlinear systems: concepts and definitions

We introduce a new class of nonlinear systems called "finitely discretizable". For a finitely discretizable nonlinear system, any trajectory is completely determined by a finite number of the state derivatives. In the polynomial case, using the notion of dilations, we give sufficient conditions for a nonlinear system to be finitely discretizable and we relate this result to nilpotent Lie algebra of vector fields. We show that multirate sampling techniques can be an efficient tool to deal with the control problem of finitely discretizable systems. We conclude by some examples illustrating the relevance of finitely discretizable systems within the framework of control theory.