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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 1945964, 14 pages
http://dx.doi.org/10.1155/2016/1945964
Research Article

Nonfragile Robust Model Predictive Control for Uncertain Constrained Systems with Time-Delay Compensation

Xi’an Institute of High-Tech, Xi’an 710025, China

Received 4 February 2016; Revised 6 June 2016; Accepted 13 June 2016

Academic Editor: Gabriele Cazzulani

Copyright © 2016 Wei Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study investigates the problem of asymptotic stabilization for a class of discrete-time linear uncertain time-delayed systems with input constraints. Parametric uncertainty is assumed to be structured, and delay is assumed to be known. In Lyapunov stability theory framework, two synthesis schemes of designing nonfragile robust model predictive control (RMPC) with time-delay compensation are put forward, where the additive and the multiplicative gain perturbations are, respectively, considered. First, by designing appropriate Lyapunov-Krasovskii (L-K) functions, the robust performance index is defined as optimization problems that minimize upper bounds of infinite horizon cost function. Then, to guarantee closed-loop stability, the sufficient conditions for the existence of desired nonfragile RMPC are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.