Region of convergence expansion of a robust model predictive controller

In this paper a gain scheduling method is proposed for robust model predictive control of a useful class of nonlinear discrete-time systems. The system is composed of a linear model perturbed by an additive state-dependent nonlinear term. Robust model predictive controllers are designed in the literature to compensate for the uncertainty of the system. In order to enlarge the region of convergence it is assumed that system has several equilibrium points and multiple robust controllers are designed. By switching between the controllers it is verified that the region of convergence shall be enlarged, while the overall stability of the system is preserved. In the proposed method, the stability analysis based on Lyapunov functions for each level set is performed, while state feedback control law is designed by minimization of a desired cost function formed in linear matrix inequalities. The simulation results show the applicability of the proposed method.