Off-line formulation of robust model predictive control based on several Lyapunov functions

It has been recognized that the dilation of the LMI characterizations has new potentials in dealing with such involved problems as multiobjective control, robust performance analysis or synthesis for real polytopic uncertainty and so on. In the model predictive control (MPC) area, Cuzzola et al. (2002) 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 compared to the other well-known techniques is the reduced conservativeness. However, this approach also increases the online computational demand, which partially limits its practicality. In this paper, an offline approach is proposed to reduce such online computational demand substantially. The approach is based on the concept of the asymptotically stable invariant ellipsoids and the closed-loop robust stability is guaranteed.