A group-theoretic approach to discrete-time non-linear controllability

The controllability of discrete-time non-linear systems is studied through the use of Ritt´s formal differential groups which were introduced thirty years ago. A condition for weak local controllability is given in terms of Lie algebra. It is very similar to the one obtained in the continuous-time case. In the case of regular (or bilinear) systems this analysis leads to Lie group techniques. Various examples are discussed.