Computational complexity reduction for robust model predictive control

Recently, it has been recognized that the dilation of the LMI characterizations has new potentials in dealing with such involved problems as multi-objective control, robust performance analysis or synthesis for real polytopic uncertainty and so on. In MPC area, Cuzzola et al. have proposed a technique which is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty polytope. The main advantage of this approach with respect to the other well-known techniques is the reduced conservativeness. However, this approach also increases the on-line computational complexity, which partially limits its practicality. In this paper a novel approach by using convex combinations is addressed in order to reduce such on-line computational complexity substantially, with guaranteed robust stability of the closed-loop system, and by using the concept of the asymptotically stable invariant ellipsoids.