I. Necoara, B. De Schutter, T.J.J. van den Boom, and J. Hellendoorn, "Robustly stabilizing MPC for perturbed PWL systems: Extended report," Tech. rep. 05-004a, Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands, 6 pp., Feb. 2005. A short version of this paper has been published in the 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.
In this paper we derive two robustly stable model predictive control (MPC) schemes for the class of piecewise linear (PWL) and hybrid systems. We assume that the plant model is subject to unknown but bounded disturbances and the states of the system can be measured or estimated. We derive a piecewise feedback controller based on linear matrix inequalities (LMI) that stabilizes the nominal system. Further we develop an algorithm for constructing a convex robustly positively invariant (RPI) set for the system. Using this convex RPI set as a terminal set we propose first a min-max feedback MPC scheme with known mode based on a dual-mode approach that stabilizes the system. The second robustly stable MPC scheme is based on a semi-feedback controller, but this time the mode of the system is unknown. Extension of the results from this paper to hybrid systems is also discussed.