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Mathematical Problems in Engineering
Volume 2011, Article ID 904914, 16 pages
Research Article

State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete-Time Systems

1Department of Marine Engineering, Shanghai Maritime University, Shanghai 200135, China
2Department of Automation, Shanghai Jiaotong University, Shanghai 200240, China
3Department of Electronic Information Engineering, Changzhou College of Information Technology, Changzhou 213164, China

Received 26 November 2010; Revised 18 February 2011; Accepted 2 April 2011

Academic Editor: Cristian Toma

Copyright © 2011 Wentao Chen 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 considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method so that the closed-loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer-based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.