Further results on 'Robust MPC using Linear Matrix Inequalities'

This paper presents a novelmethod for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and \(\mathcal{H}_\infty\) control design. This relation shows that the LMI-based optimal solution of the \(\mathcal{H}_\infty\) synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.