This article concerns the feedback control of discrete-time systems subject to disturbances and uncertainties in both model parameters and signal measurements. The uncertainties are assumed to be unknown but bounded and thus characterised by closed intervals or sets. The main result is a new approach to design a feedback controller keeping the system state in a target set. First, a method is proposed that computes minimal enclosures of the set of reachable states, which are consistent with the uncertain input and output measurements and the system dynamics. Then, a control method to keep the current state set in the target set is developed, which extends control techniques based on invariant polyhedra. The method is illustrated by a mobile robot experiment.