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Synchronization criteria for neural networks with proportional delays via quantized control

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Abstract

With the aid of quantized control, this paper presents new synchronization criteria of neural networks (NNs) with proportional delays. The NNs with constant delays and variable coefficients are obtained, which are equivalently transformed from the NNs with proportional delays. Taking the communication limitation into account, quantized controllers which include state feedback controllers and quantized adaptive controllers are designed for the first time for solving synchronization problem of NNs with proportional delays. By constructing Lyapunov function, utilizing new controllers, and applying new analytical methods, several criteria are derived to realize synchronization. Here, the obtained synchronization of NNs with proportional delays is not called exponential synchronization since the convergence rate is not fixed. Finally, numerical simulations are offered to substantiate our theoretical results.

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Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61374078, 61673078, 61633011, the Foundation and Frontier Project of Chongqing under Grant No. cstc2015jcyjA00027.

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Authors and Affiliations

  1. National and Local Joint Engineering Laboratory of Intelligent Transmission and Control Technology (Chongqing), College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Wanli Zhang, Chuandong Li & Shiju Yang

  2. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Xinsong Yang

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  1. Wanli Zhang
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  2. Chuandong Li
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  3. Shiju Yang
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  4. Xinsong Yang
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Correspondence to Chuandong Li.

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Zhang, W., Li, C., Yang, S. et al. Synchronization criteria for neural networks with proportional delays via quantized control. Nonlinear Dyn 94, 541–551 (2018). https://doi.org/10.1007/s11071-018-4376-x

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  • DOI: https://doi.org/10.1007/s11071-018-4376-x

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