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Synchronization of delayed neural networks with Lévy noise and Markovian switching via sampled data

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Abstract

In this paper, the problem of synchronization via sampled-data control is considered for stochastic delayed neural networks with Lévy noise and Markovian switching. The purpose of the problem addressed is to derive a sufficient condition and a sampled-data control law such that the dynamics of the error system is stable in mean square, and thus the synchronization can be achieved for the master system and the slave system. By generalized Itô’s formula and the construction of Lyapunov functional, an LMI-based sufficient condition is established to ensure the synchronization of the two systems. The control law is determined simultaneously, which depends on the switching mode, time delay, and the upper bound of sampling intervals. A numerical example is provided to verify the usefulness of the proposed criterion.

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Acknowledgments

This work is partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education under grant no. 20120075120009, the Natural Science Foundation of Shanghai under Grant Nos. (15ZR1401800, 12ZR1440200), the Australian Research Council (DP140102180, LP140100471), and the 111 Project (B12018).

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Authors and Affiliations

  1. College of Information Sciences and Technology, Donghua University, Shanghai, 200051, China

    Jun Yang, Wuneng Zhou, Xueqing Yang & Xianghui Zhou

  2. School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China

    Jun Yang

  3. Engineering Research Center of Digitized Textile and Fashion Technology, Ministry of Education, Donghua University, Shanghai, 201620, China

    Wuneng Zhou

  4. College of Automation, Harbin Engineering University, Harbin, 150001, Heilongjiang, China

    Peng Shi

  5. College of Engineering and Science, Victoria University, Melbourne, VIC, 8001, Australia

    Peng Shi

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

    Hongye Su

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  1. Jun Yang
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  2. Wuneng Zhou
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  3. Peng Shi
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  4. Xueqing Yang
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  5. Xianghui Zhou
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Correspondence to Jun Yang or Wuneng Zhou.

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Yang, J., Zhou, W., Shi, P. et al. Synchronization of delayed neural networks with Lévy noise and Markovian switching via sampled data. Nonlinear Dyn 81, 1179–1189 (2015). https://doi.org/10.1007/s11071-015-2059-4

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  • DOI: https://doi.org/10.1007/s11071-015-2059-4

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