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Adaptive Synchronization of Unknown Complex Dynamical Networks with Derivative and Distributed Time-Varying Delay Couplings

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Abstract

This paper investigates the synchronization problem of unknown non-identical complex dynamical networks with derivative and distributed time-delay couplings. To deal with the unknown topological structure, a new general class of T–S fuzzy model is proposed in this paper. Then, the unknown network is presented by a fuzzy system. In order to achieve synchronization of the above fuzzy network, this paper designs a fuzzy adaptive feedback controller which is only connected with the dynamical behavior of directly related nodes. Meanwhile, a new class of fuzzy Lyapunov function is constructed in this paper. The sufficient asymptotic synchronization condition is obtained in terms of linear matrix inequality. Numerical example is given to demonstrate the effectiveness of the proposed theoretical results.

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Acknowledgements

This work is supported by National Nature Science Foundation (NNSF) of China under Grants 61573013, 61603286; the Fundamental Research Funds for the Central Universities under Grant JB160702.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, No. 245 Xidian University, Xi’an, 710126, Shanxi, China

    Xinxin Yuan, Junmin Li & Jinsha Li

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  1. Xinxin Yuan
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  2. Junmin Li
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  3. Jinsha Li
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Correspondence to Junmin Li.

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Yuan, X., Li, J. & Li, J. Adaptive Synchronization of Unknown Complex Dynamical Networks with Derivative and Distributed Time-Varying Delay Couplings. Int. J. Fuzzy Syst. 20, 1088–1097 (2018). https://doi.org/10.1007/s40815-017-0424-9

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  • DOI: https://doi.org/10.1007/s40815-017-0424-9

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