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Passivity and Passivity-Based Synchronization of Switched Coupled Reaction-Diffusion Neural Networks with State and Spatial Diffusion Couplings

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Abstract

The authors investigate the passivity problem of switched coupled reaction-diffusion neural networks (SCRDNNs) with state and spatial diffusion couplings in this paper. For the considered network model, we derive an input strict passivity (ISP) criterion and an output strict passivity (OSP) criterion respectively by constructing an appropriate Lyapunov functional and exploiting Green’s formula and some other useful inequalities. Additionally, the authors also establish the relationship between exponential stability and OSP. Moreover, a sufficient condition for achieving synchronization of the considered SCRDNNs with hybrid coupling is presented according to the deduced OSP result and the relationship between exponential stability and OSP. Finally, the correctness of the derived theoretical conclusions is illustrated by two examples with simulation results.

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Acknowledgements

The authors would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions. This work was supported in part by the National Natural Science Foundation of China under Grants 11501411, 61503010, 61403275 and 11401018, 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. Tianjin Key Laboratory of Optoelectronic Detection Technology and System, School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin, 300387, China

    Yanli Huang

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

    Shunyan Ren

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  1. Yanli Huang
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Correspondence to Yanli Huang.

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Huang, Y., Ren, S. Passivity and Passivity-Based Synchronization of Switched Coupled Reaction-Diffusion Neural Networks with State and Spatial Diffusion Couplings. Neural Process Lett 47, 347–363 (2018). https://doi.org/10.1007/s11063-017-9651-1

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