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Sampled-Data \(H_{\infty }\) Synchronization of Chaotic Lur’e Systems with Time Delay

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Abstract

This paper deals with the problem of robust \(H_{\infty }\) synchronization of chaotic Lur’e systems with time-varying delays via sampled-data control. In order to make full use of the information about sampling intervals, nonlinear functions and time-varying delays, an improved Lyapunov–Krasovskii (L–K) functional is introduced. Based on reciprocal convex combination technique, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic synchronization of the considered Lur’e system with a guaranteed \(H_{\infty }\) performance. By solving the obtained LMIs, the required sampled-data control gain matrix is obtained, which assures the asymptotic stability of the error system and reduces the effect of external disturbance according to \(H_{\infty }\) norm. Finally, the effectiveness and less conservatism of the proposed method are verified through numerical simulations of the Chua’s circuit and neural networks.

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Acknowledgments

This research work is supported by UGC-BSR Fellowship Grant No. F.4-1/2006(BSR)/ 7-27/2007(BSR) from the University Grant Commission, Government of India, New Delhi, the National Natural Science Foundation of China (Grant Nos. 61272530 and 11072059), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2012741) and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant Nos. 20110092110017 and 20130092110017).

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Authors and Affiliations

  1. Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096, China

    Jinde Cao

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jinde Cao

  3. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, Tamilnadu, India

    R. Sivasamy & R. Rakkiyappan

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  1. Jinde Cao
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Correspondence to Jinde Cao.

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Cao, J., Sivasamy, R. & Rakkiyappan, R. Sampled-Data \(H_{\infty }\) Synchronization of Chaotic Lur’e Systems with Time Delay. Circuits Syst Signal Process 35, 811–835 (2016). https://doi.org/10.1007/s00034-015-0105-6

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