Accessibility and feedback linearization of discrete-time systems

The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas for nonlinear continuous-time systems the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recast through the language of differential forms. This yields a solution which is completely constructive. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system