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Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data

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Abstract

This paper investigates the synchronization problem of neural networks with time-varying delay under sampled-data control in the presence of a constant input delay. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. A simple and less conservative synchronization criterion is given to ensure the master systems synchronize with the slave systems by using the linear matrix inequality (LMI) approach. The design method of the desired sampled-data controller is also proposed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

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Acknowledgements

The work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0009373). This work was also supported in part by the National Natural Science Foundation of China under Grant 61174029.

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Authors and Affiliations

  1. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749, Republic of Korea

    Zheng-Guang Wu & Ju H. Park

  2. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou, Zhejiang, 310027, P.R. China

    Zheng-Guang Wu, Hongye Su & Jian Chu

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  1. Zheng-Guang Wu
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  2. Ju H. Park
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Correspondence to Ju H. Park.

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Wu, ZG., Park, J.H., Su, H. et al. Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data. Nonlinear Dyn 69, 2021–2030 (2012). https://doi.org/10.1007/s11071-012-0404-4

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  • DOI: https://doi.org/10.1007/s11071-012-0404-4

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