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Lagrange Stability of BAM Quaternion-Valued Inertial Neural Networks via Auxiliary Function-Based Integral Inequalities

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Abstract

This article is concerned with the global exponential stability in Lagrange sense of bidirectional associative memory quaternion-valued inertial neural networks by non-reduced order and undecomposed approach. Firstly, for the completeness of the information carried by the model, the inertial term is not reduced in order, and the quaternion is not decomposed into four real values or two complex values. Then, for the sake of reducing the conservatism, auxiliary function-based inequalities and reciprocally convex inequality are applied to the set of quaternion. And several criteria for Lagrange stability are acquired in the form of linear matrix inequalities. Ultimately, numerical simulations are proved the feasibility of the outcomes.

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Acknowledgements

The authors are grateful for the support of the National Natural Science Foundation of China (Grant Nos. 61304162, 11601268).

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Authors and Affiliations

  1. College of Science, China Three Gorges University, Yichang, 443002, Hubei, China

    Rui Zhao, Baoxian Wang & Jigui Jian

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  1. Rui Zhao
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  2. Baoxian Wang
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  3. Jigui Jian
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Correspondence to Baoxian Wang.

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Zhao, R., Wang, B. & Jian, J. Lagrange Stability of BAM Quaternion-Valued Inertial Neural Networks via Auxiliary Function-Based Integral Inequalities. Neural Process Lett 54, 1351–1369 (2022). https://doi.org/10.1007/s11063-021-10685-6

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