Piecewise affinity of min-max MPC with bounded additive uncertainties and a quadratic criterion

This brief shows how a min-max MPC with bounded additive uncertainties and a quadratic cost function results in a piecewise affine and continuous control law. Proofs based on properties of the cost function and the optimization problem are given. The boundaries of the regions in which the state space can be partitioned are also treated. The results are illustrated by an example.