arXiv:2512.04239v3 Announce Type: replace Abstract: Periodic operation often emerges as the economically optimal mode in industrial processes subject to varying economic or environmental conditions. This paper proposes a robust model predictive control (MPC) framework for uncertain systems described by polytopic linear difference inclusions (LDIs), whose dynamics evolve as convex combinations of finitely many linear control systems subject to additive disturbances. The robust control problem is formulated as a convex optimization program over configuration-constrained polytopic tubes, with the objective of tracking a periodic tube that is optimal for a given economic criterion. Artificial variables embedded in the formulation ensure recursive feasibility and robust constraint satisfaction under changes in the economic criterion, and convergence to the optimal periodic tube when the criterion remains constant. To improve computational efficiency, we introduce a quadratic upper approximation of the periodic cost under a Lipschitz continuity assumption, yielding a Quadratic Program (QP) that preserves the above theoretical guarantees. The approach is demonstrated on an illustrative example and an eight-state ball--plate system.