Robust model predictive control of discrete-time uncertain linear systems with persistent disturbances

Robust model predictive control of a discrete-time uncertain linear system is considered. Both polytopic and structured uncertainties are taken into account in the system model. Besides, the system is subject to persistent disturbances. Noting that robust positively invariant (RPI) set plays an important role in both recursive feasibility and stability analysis, computation of a RPI set is developed. Based on this result, an online predictive controller is proposed. The closed-loop control system is guaranteed to be input-to-state stable. A numerical example is given to illustrate the effectiveness of the controller.