This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced, The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems.