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Journal of Applied Mathematics
Volume 2013, Article ID 319415, 8 pages
Research Article

Memory State-Feedback Stabilization for a Class of Time-Delay Systems with a Type of Adaptive Strategy

Lin Chai1,2 and Shumin Fei1,2

1Key Laboratory of Measurement and Control of Complex Systems of Engineering, Southeast University, Nanjing 210096, China
2School of Automation, Southeast University, Nanjing 210096, China

Received 31 December 2012; Revised 20 May 2013; Accepted 13 June 2013

Academic Editor: Constantinos Siettos

Copyright © 2013 Lin Chai and Shumin Fei. 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.


Stabilization of a class of systems with time delay is studied using adaptive control. With the help of the “error to error” technique and the separated “descriptor form” technique, the memory state-feedback controller is designed. The adaptive controller designed can guarantee asymptotical stability of the closed-loop system via a suitable Lyapunov-Krasovskii functional. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality (LMI) design approach. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.