In this paper, the explicit constrained min-max MPC problem is solved by an algorithm which is based on a discrete-time linear system with uncertain disturbances. Since the maximum of the quadratic cost function is only attained at extreme point of the disturbance set, the designed method is proposed in two different kinds of active extreme point sets, which correspond to two kinds of state regions. As a result, the state space is partitioned into polyhedral regions and a piecewise linear feedback control law has been defined over resulting cones.
Complementarity and passivity for piecewise linear feedback systems