Linear matrix inequalities and polyhedral invariant sets in constrained robust predictive control

Robust predictive control in the presence of polytopic model uncertainty has been tackled through the use of linear matrix inequalities and ellipsoidal invariant sets. Earlier work in this area restricted the prediction class to state feedback and did not make use of a control horizon; furthermore the computational load in this approach was excessive. Both these problems can be overcome through the use of an autonomous but augmented system for the purposes of prediction. Recent work considered the use of a control horizon and polyhedral sets, and here we extend this approach to the more efficient formulation based on the autonomous system predictions. In addition, it is shown that robustness with respect to bounded disturbances can be handled in the same framework of autonomous system predictions and an appropriate predictive control algorithm is suggested. This paper is concluded by means of a numerical example which provide comparison of the result of the paper with those proposed elsewhere.