A novel set-membership control strategy is investigated for a class of discrete time-varying systems with unknown-but-bounded noises. Different from some existing set-membership estimation based control methods, the proposed control strategy is designed by using state estimation sets instead of some specific estimation points. The controlled performance requirement is modelled as a new set-membership performance constraint which ensures that the controlled output meets the requirement at any time instant. First, the set-membership filtering method is used for obtaining the ellipsoidal state estimation set. Second, a set-membership controller is constructed by utilising the state estimation which is arbitrarily chosen from the corresponding estimation set. Accordingly, sufficient conditions are derived such that the controlled system is asymptotically stable and satisfies the proposed performance constraint in the presence of unknown-but-bounded noises at each time instant. Then, a constructive computational algorithm is provided to describe the proposed control strategy. Finally, illustrative simulation examples are presented to demonstrate the effectiveness of the proposed method.