This paper presents a robust model predictive control (MPC) algorithm for stable, linear plants described by a state-space model. Model uncertainty is parameterized by an infinite-dimensional set of possible plants. Robust stability is achieved by adding cost function constraints that prevent the sequence of optimal controller costs from increasing for the true plant. The optimal input is re-computed at each time step by solving a convex semi-infinite program. The solution is Lipschitz continuous in the state at the origin; as a result the closed loop system is exponentially stable and asymptotically decaying disturbances can be rejected. Simulation results illustrate performance of the algorithm relative to other methods when the elements of the input matrix lie in an elliptical uncertainty region.