Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays

In this paper, the finite-time stabilization and destabilization of a class of quaternion-valued neural networks (QVNNs) with discrete delays are investigated. In order to surmount the difficulty of noncommutativity of quaternion, a new vector matrix differential equation (VMDE) is proposed by emplo...

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Published inComplexity (New York, N.Y.) Vol. 2020; no. 2020; pp. 1 - 12
Main Authors Qiu, Jianlong, Tu, Zhengwen, Peng, Tao, Duan, Huiling
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Wiley
Subjects
Analysis
Control stability
Control systems design
Controllers
Destabilization
Differential equations
Liapunov functions
Mathematical analysis
Matrix algebra
Matrix methods
Neural networks
Nonlinear control
Quaternions
Stability analysis
China
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ISSN1076-2787
1099-0526
DOI10.1155/2020/8526030

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Summary:In this paper, the finite-time stabilization and destabilization of a class of quaternion-valued neural networks (QVNNs) with discrete delays are investigated. In order to surmount the difficulty of noncommutativity of quaternion, a new vector matrix differential equation (VMDE) is proposed by employing decomposition method. And then, a nonlinear controller is designed to stabilize the VMDE in a finite-time interval. Furthermore, under that controller, the finite-time stability and instability of the QVNNs are analyzed via Lyapunov function approach, and two criteria are derived, respectively; furthermore, the settling time is also estimated. At last, by two illustrative examples we verify the correctness of the conclusions.
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ISSN:1076-2787
1099-0526
DOI:10.1155/2020/8526030