The adaptive robust control design problem for discrete systems is addressed in this article. A measure of the system uncertainty is quantified through the application of the set membership (SM) identification scheme. The SM estimator identifies a feasible convex set (parallepiped) of parameters which is consistent with the data and the model structure. Based on these parameters, a robust stabilising controller computes the feasible set of stabilising controller gains. The adaptation mechanism attempts to place the closed loop poles at a certain region inside the unit disc. Simulation studies are offered to validate the efficiency of the proposed method.