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Volume 7
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10.3390/math7020138
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Article

Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays

by
Zhixin Zhang
1,
Yufeng Zhang
1,
Jia-Bao Liu
2,3,* and
Jiang Wei
1
1
School of Mathematics Sciences, Anhui University, Hefei 230601, China
2
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
3
School of Mathematics, Southeast University, Nanjing 210096, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(2), 138; https://doi.org/10.3390/math7020138
Submission received: 1 December 2018 / Revised: 24 January 2019 / Accepted: 30 January 2019 / Published: 1 February 2019
(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2019)
Versions Notes

Abstract

In this paper, the global asymptotical stability of Riemann-Liouville fractional-order neural networks with time-varying delays is studied. By combining the Lyapunov functional function and LMI approach, some sufficient criteria that guarantee the global asymptotical stability of such fractional-order neural networks with both discrete time-varying delay and distributed time-varying delay are derived. The stability criteria is suitable for application and easy to be verified by software. Lastly, some numerical examples are presented to check the validity of the obtained results.
Keywords: time-varying delay; global asymptotical stability; fractional-order; neural networks; linear matrix inequality time-varying delay; global asymptotical stability; fractional-order; neural networks; linear matrix inequality

Share and Cite

MDPI and ACS Style

Zhang, Z.; Zhang, Y.; Liu, J.-B.; Wei, J. Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays. Mathematics 2019, 7, 138. https://doi.org/10.3390/math7020138

AMA Style

Zhang Z, Zhang Y, Liu J-B, Wei J. Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays. Mathematics. 2019; 7(2):138. https://doi.org/10.3390/math7020138

Chicago/Turabian Style

Zhang, Zhixin, Yufeng Zhang, Jia-Bao Liu, and Jiang Wei. 2019. "Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays" Mathematics 7, no. 2: 138. https://doi.org/10.3390/math7020138

APA Style

Zhang, Z., Zhang, Y., Liu, J.-B., & Wei, J. (2019). Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays. Mathematics, 7(2), 138. https://doi.org/10.3390/math7020138

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