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State Estimation of Quaternion-Valued Neural Networks with Leakage Time Delay and Mixed Two Additive Time-Varying Delays

  • Libin Liu
  • Xiaofeng ChenEmail author
Article
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Abstract

In this paper, the state estimation of quaternion-valued neural networks (QVNNs) with leakage time delay, both discrete and distributed two additive time-varying delays is studied. By considering the QVNNs as a whole, instead of decomposing it into two complex-valued neural networks or four real-valued neural networks. Via constructing suitable Lyapunov–Krasovskii functionals, combining free weight matrix, reciprocally convex approach, and matrix inequalities, the sufficient criteria for time delays are given in the form of quaternion-valued linear matrix inequalities and complex-valued linear matrix inequalities. Some observable output measurements are used to estimate the state of neurons, which ensures the global asymptotic stability of the error-state system. Finally, the effectiveness of theoretical analysis is illustrated by a numerical simulation.

Keywords

Quaternion-valued neural networks Linear matrix inequalities State estimation Additive time-varying delays 

Notes

Acknowledgements

This work was supported in part by the Natural Science Foundation of Chongqing under Grants cstc2018jcyjAX0606, cstc2017jcyjA1353 and cstc2017jcyjAX0172, and in part by the Natural Science Foundation of Chongqing Municipal Education Commission under Grants KJQN201800740 and KJ1705118.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.College of FinanceChongqing Technology and Business UniversityChongqingChina
  2. 2.Department of Economics and ManagementChongqing Jiaotong UniversityChongqingChina

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