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Mathematical Problems in Engineering
Volume 2014, Article ID 409863, 9 pages
Research Article

Memory State Feedback RMPC for Multiple Time-Delayed Uncertain Linear Systems with Input Constraints

1Department of Automatic Control, Xi’an Research Institute of High-Tech, Xi’an 710025, China
2College of Mechatronics and Automation, National University of Defense Technology, Changsha 410073, China

Received 11 December 2013; Revised 1 March 2014; Accepted 13 March 2014; Published 13 April 2014

Academic Editor: Shuhui Bi

Copyright © 2014 Wei-Wei Qin 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.


This paper focuses on the problem of asymptotic stabilization for a class of discrete-time multiple time-delayed uncertain linear systems with input constraints. Then, based on the predictive control principle of receding horizon optimization, a delayed state dependent quadratic function is considered for incorporating MPC problem formulation. By developing a memory state feedback controller, the information of the delayed plant states can be taken into full consideration. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Then, based on the Lyapunov-Krasovskii function, a delay-dependent sufficient condition in terms of linear matrix inequality (LMI) can be derived to design a robust MPC algorithm. Finally, the digital simulation results prove availability of the proposed method.