On the piecewise linear nature of constrained min-max model predictive control with bounded uncertainties

As shown by the authors in a previous paper, min-max MPC with a quadratic criterion, bounded additive uncertainties and a linear prediction model, results in a piecewise linear controller, which can be formulated in explicit form. This paper shows that a constrained min-max MPC with bounded additives uncertainties and a quadratic cost is also a piecewise linear control law. Proofs based on properties of the cost function and the optimization problem is given. The results are illustrated by a simulation example.