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Synchronization and exponential estimates of complex networks with mixed time-varying coupling delays

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Abstract

Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities (LMIs). A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed time-varying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, PRC

    Yang Dai, Yun-Ze Cai & Xiao-Ming Xu

  2. University of Shanghai for Science and Technology, Shanghai, 200093, PRC

    Xiao-Ming Xu

  3. Shanghai Academy of Systems Science, Shanghai, 200093, PRC

    Xiao-Ming Xu

Authors
  1. Yang Dai
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  2. Yun-Ze Cai
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  3. Xiao-Ming Xu
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Corresponding author

Correspondence to Yang Dai.

Additional information

This work was supported by the National Key Fundamental Research Program (No. 2002CB312201-03) and the National Natural Science Foundation of China (No. 60575036).

Yang Dai received the B. Sc. and M. Sc. degrees from Liaoning Shihua University, PRC in 2002 and 2005, respectively. She is currently a Ph. D. candidate in control theory and control engineering, Shanghai Jiao Tong University, PRC.

Her research interests include synchronization of complex networks and time delay system.

Yun-Ze Cai received the Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, PRC in 2003. Currently, she is an associate professor at the Department of Automation, Shanghai Jiao Tong University.

Her research interests include robust control for delay systems, robust filter design, and wavelet denoising.

Xiao-Ming Xu received the Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, PRC in 1987. Currently, he is the president and professor of University of Shanghai for Science and Technology, PRC, and the president of Shanghai Academy of Systems Science, PRC.

His research interests include predictive control, process control, and robust control theory and application.

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Dai, Y., Cai, YZ. & Xu, XM. Synchronization and exponential estimates of complex networks with mixed time-varying coupling delays. Int. J. Autom. Comput. 6, 301–307 (2009). https://doi.org/10.1007/s11633-009-0301-6

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  • DOI: https://doi.org/10.1007/s11633-009-0301-6

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