Robust One-step Model Predictive Control for Discrete Time-delay Systems ?

In this paper a robust one-step model predictive control (MPC) scheme is developed for discrete time-delay systems with polytopic-type uncertainty. The proposed MPC is obtained by minimizing a new cost function that includes multi-terminal weighting terms, subject to constraints on input. This MPC scheme allows the first move u(k|k) to be separated from the control moves governed by a state feedback law, which can reduce conservatism and improve feasibility and optimality. A linear matrix inequality (LMI) approach is applied to the controller synthesis. It can be shown that the proposed model predictive controller guarantees closed-loop stability. Simulation results are given to illustrate the performance of the proposed algorithm.