ABSTRACT
This chapter introduces synthesis approaches of robust Model predictive control (MPC) for systems with polytopic description. "Explicitly" means that the uncertainty is considered in the optimization problem of MPC. The uncertainty of the model is overcome by feedback correction or on-line refreshment of the model. Since a nominal model is adopted, the existing stability analysis is mainly for the nominal systems. The studies on the robustness of MPC and robust MPC can be classified as robustness analysis and robustness synthesis. Polytope can be obtained by two different manners. At different operating points, or at different time periods, input/output data can be obtained for the same system. Linear matrix inequality (LMI) is especially suitable in the analysis and design works based on the polytopic description.
