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Passivity and Robust Passivity of Delayed Cohen–Grossberg Neural Networks With and Without Reaction–Diffusion Terms

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Abstract

In this paper, we address the passivity and robust passivity problems for delayed Cohen–Grossberg neural networks (DCGNNs) both with and without reaction–diffusion terms. First, by resorting to appropriate Lyapunov functionals combined with some inequality techniques, some passivity conditions for DCGNNs without the reaction–diffusion terms are derived. Moreover, considering that parameter uncertainties may appear in neural networks, we also study the robust passivity of DCGNNs. In addition, we extend these derived results to the model of DCGNNs with reaction–diffusion terms. The validity and advantages of the theoretical results are demonstrated by three numerical examples.

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Acknowledgements

The authors would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions. In addition, they also wish to express their sincere appreciation to Prof. Jinliang Wang for the fruitful discussions with him and good suggestions which helped to improve this paper. This work was supported in part by the National Natural Science Foundation of China under Grants 11501411, 61403275, 61503010 and 61773285, in part by the Natural Science Foundation of Tianjin, China, under Grant 15JCQNJC04100, and in part by the Aeronautical Science Foundation of China (No. 2016ZA51001).

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Authors and Affiliations

  1. School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin, 300387, China

    Weizhong Chen

  2. School of Computer Science and Software Engineering, Tianjin Key Laboratory of Optoelectronic Detection Technology and System, Tianjin Polytechnic University, Tianjin, 300387, China

    Yanli Huang

  3. School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin, 300387, China

    Shunyan Ren

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  1. Weizhong Chen
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  2. Yanli Huang
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Correspondence to Yanli Huang.

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Chen, W., Huang, Y. & Ren, S. Passivity and Robust Passivity of Delayed Cohen–Grossberg Neural Networks With and Without Reaction–Diffusion Terms. Circuits Syst Signal Process 37, 2772–2804 (2018). https://doi.org/10.1007/s00034-017-0693-4

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