A Multistep Multiellipsoid Approach of the Dynamic Output Feedback MPC

This article considers the dynamic output feedback model predictive control for the constrained Takagi–Sugeno (T-S) model with bounded disturbance. Unlike the existing approach where the robust positively invariant set is characterized by a single ellipsoid, we characterize it by the intersection of multiple ellipsoids, each corresponds to a vertex submodel of the T-S model realization. The previous single ellipsoid is then an inner approximation of the intersection of multiple ellipsoids in this article. Therefore, the performance can be improved. We also generalize the multiellipsoid approach to the previous multistep approach and formulate the so-called multistep multiellipsoid approach in this article, which can further enlarge the feasibility region and enhance the performance. The recursive feasibility and the convergence of the approach are guaranteed. The proposed approaches are compared through two numerical problems to show their effectiveness.