I. Necoara, B. De Schutter, T.J.J. van den Boom, and J. Hellendoorn, "Robustly stabilizing MPC for perturbed PWL systems," Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 (CDC-ECC'05), Seville, Spain, pp. 3759-3764, Dec. 2005.
This paper deals with robustly stable model predictive control (MPC) of the class of piecewise linear systems. A piecewise linear feedback controller, that stabilizes the nominal system, is derived from linear matrix inequalities. Further, an algorithm is designed for constructing a polyhedral robustly positively invariant set for the system. First, a min-max feedback MPC scheme with known mode, based on a dual-mode approach that stabilizes the system, is presented. The second robustly stable MPC scheme is based on a semi-feedback controller, but this time the mode of the system is unknown.