A backstepping-like approach to adaptive control in discrete time

Nonlinear adaptive control in discrete time is still largely open. The exis ting results deal with particular cases and are mainly based upon tradition al estimation techniques issued from the linear literature. In this paper, combining a backstepping strategy and "a posteriori" estimation concepts, a novel approach for achieving adaptive stabilization is proposed. It can di rectly be applied to a class of nonlinear discrete-time systems that, analo gous to the continuous-time context, are said to be in a parametric strict- feedback form. Necessary, and sufficient geometric-conditions guaranteeing the equivalence of a general discrete-time dynamics to the parametric stric t-feedback form or to some related classes of dynamics are also proposed.