A model predictive scheme to integral controller design for uncertain LTI systems with nonzero reference

A model predictive method is developed to tune an integral controller for uncertain systems subjected to constrained input signals. For this purpose, a stabilizing integral controller is firstly designed for linear time-invariant (LTI) systems with polytopic uncertainty. The integral controller gains can be determined via a feasible solution of a linear matrix inequality (LMI). Then, a predictive control is incorporated into the integral controller synthesis through an optimization problem subjected to some LMI constraints. The suggested control is successfully applied to a typical uncertain system and an uncertain chemical reactor. The effectiveness of the proposed technique will be shown in comparison with other control methods.