A direct adaptive non-linear control framework for discrete-time multivariable non-linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non-linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant. In the case of bounded energy l 2 disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input-output map. Finally, three illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.