This paper presents two robust model predictive control (MPC) algorithms for linear integrating plants described by a state-space model. The first formulation focuses on steady-state offset whereas the second minimizes output deviations over the entire prediction horizon. The input matrix parameters of the plant are assumed to lie in a set defined by an ellipsoidal bound. Robustness is achieved through the addition of constraints that prevent the sequence of the optimal controller costs from increasing for the true plant. The resulting optimization problems solved at each time step are convex and highly structured. A simulation example compares the performance of these algorithms with those based on minimizing the worst-case controller cost.