Nonfragile robust model predictive control for uncertain constrained time-delayed system with compensations

This paper concerns the nonfragile robust model predictive control problem for discrete uncertain linear time-delayed systems subjected to input constraint and controller gain perturbation. By using the Lyapunov-Krasovskii stability theory and linear matrix inequality approach, sufficient conditions for nonfragile robust model predictive control with delayed state compensation are derived to asymptomatically stabilize the closed-loop system with guaranteed H∞ and H2 performance index for all admissible polytopic uncertainties, external disturbance, single state and input delay, and additive or multiplicative gain perturbation. Furthermore, the input constraint and the recursive feasibility are handled via additional constrainted conditions. Finally, two numerical examples are given to illustrate the effectiveness of the proposed approach.