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Pinning lag synchronization of complex dynamical networks with known state time-delay and unknown channel time-delay

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Abstract

In this paper, a linear and adaptive feedback pinning strategy is used to study the lag synchronization of complex dynamical networks with known state time-delay and unknown channel time-delay. Firstly, based on the Lyapunov stability theory, a novel Lyapunov functional, which involves the estimated error \(\hat{e}_{i}(t)\) rather than the general synchronization error \(e_{i}(t)\), is constructed. Secondly, in view of the unknown information of the channel time-delay, two available pinning controllers are designed such that the considered networks achieve lag synchronization. Furthermore, by a proper adaptation mechanism, we estimate the unknown channel time-delay successfully under the case that the initial value of the estimated channel time-delay is larger than true channel time-delay, i.e., \(\hat{\tau }(0)>\tau \) and the another case \(\hat{\tau }(0)<\tau \). Finally, the effectiveness and correctness of the lag synchronization criteria are verified through two simulation experiments.

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Acknowledgements

The authors would like to thank the editors and the reviewers for their valuable suggestions and comments which have led to a much improved paper. This work was financially supported by the National Natural Science Foundation of China No. 61533006.

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  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Huilan Yang, Lan Shu & Shouming Zhong

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  1. Huilan Yang
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  2. Lan Shu
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  3. Shouming Zhong
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Correspondence to Huilan Yang.

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Yang, H., Shu, L. & Zhong, S. Pinning lag synchronization of complex dynamical networks with known state time-delay and unknown channel time-delay. Nonlinear Dyn 89, 1793–1802 (2017). https://doi.org/10.1007/s11071-017-3552-8

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  • DOI: https://doi.org/10.1007/s11071-017-3552-8

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