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Mathematical Problems in Engineering
Volume 2009, Article ID 732181, 24 pages
Research Article

Further Results Concerning Delay-Dependent Control for Uncertain Discrete-Time Systems with Time-Varying Delay

1Research Institute of Automation, Qufu Normal University, Qufu 273165, Shandong, China
2School of Computer Science and Technology, Ludong University, Yantai 264025, Shandong, China

Received 20 March 2009; Revised 27 June 2009; Accepted 10 November 2009

Academic Editor: Tamas Kalmar-Nagy

Copyright © 2009 Guangdeng Zong 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 addresses the problem of control for uncertain discrete-time systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output. Attention is focused on the design of a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and reduces the effect of the disturbance input on the controlled output to a prescribed level irrespective of all the admissible uncertainties. By introducing some slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the reduced conservatism and lower computational burden than the previous results.