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New results on finite-time stability of fractional-order neural networks with time-varying delay

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Abstract

In this paper, we propose an analytical approach based on the Laplace transform and Mittag–Leffler functions combining with linear matrix inequality techniques to study finite-time stability of fractional-order neural networks (FONNs) with time-varying delay. The concept of finite-time stability is extended to the fractional-order neural networks and the delay function is assumed to be non-differentiable, but continuous and bounded. We first prove some important lemmas on the existence of solutions and on estimation of the Caputo derivative of specific quadratic functions. Then, new delay-dependent sufficient conditions for finite-time stability of FONNs with time-varying delay are derived in terms of a tractable linear matrix inequality and Mittag–Leffler functions. Finally, a numerical example with simulations is provided to demonstrate the effectiveness and validity of the theoretical results.

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Acknowledgements

This paper was written when the authors were studying at the Vietnam Institute for Advanced Study in Mathematics (VIASM). We sincerely thank the Institute for support and hospitality. The research of N.T. Thanh and V.N. Phat is supported by National Foundation for Science and Technology Development (No. 101.01-2021.01). The research of P. Niamsup is supported by the Chiang Mai University, Thailand. The authors wish to thank the associate editor and anonymous reviewers for valuable comments and suggestions, which allowed us to improve the paper.

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Thanh, N.T., Niamsup, P. & Phat, V.N. New results on finite-time stability of fractional-order neural networks with time-varying delay. Neural Comput & Applic 33, 17489–17496 (2021). https://doi.org/10.1007/s00521-021-06339-2

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  • DOI: https://doi.org/10.1007/s00521-021-06339-2

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