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Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach

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Abstract

In this paper, we study the problem of passivity analysis of fractional-order neural networks (FONNs) with a time-varying delay. By using the Razumikhin fractional-order theorem, we first derive an improved sufficient criterion for asymptotic stability of FONNs with a bounded time-varying delay. Then, based on the proposed stability criterion and some auxiliary properties of fractional calculus, a delay-dependent condition is established to ensure the passivity of the considered system. These conditions are order-dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved in polynomial time by using the existing convex algorithms. Some numerical examples are provided to show the effectiveness of the obtained results.

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Acknowledgements

The author would like to thank the editor(s) and anonymous reviewers for their constructive comments which helped to improve the present paper. The research of Nguyen Thi Thanh Huyen is funded by Ministry of Education and Training of Vietnam (B2020-TNA-13).

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Authors and Affiliations

  1. Institute of Research and Development, Duy Tan University, Danang, 550000, Vietnam

    Nguyen Huu Sau

  2. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mai Viet Thuan

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mai Viet Thuan

  4. Department of Mathematics and Informatics, Thainguyen University of Sciences, Thainguyen, Vietnam

    Nguyen Thi Thanh Huyen

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  1. Nguyen Huu Sau
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  2. Mai Viet Thuan
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Correspondence to Mai Viet Thuan.

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Sau, N.H., Thuan, M.V. & Huyen, N.T.T. Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach. Circuits Syst Signal Process 39, 5906–5925 (2020). https://doi.org/10.1007/s00034-020-01450-6

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