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

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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Main Authors: Huiling Duan, Tao Peng, Zhengwen Tu, Jianlong Qiu
Format: Article
Language:English
Published: Hindawi-Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/8526030
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spelling doaj-7f04aa548fda466fa83f7f7bde0f85972020-11-25T03:50:44ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/85260308526030Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete DelaysHuiling Duan0Tao Peng1Zhengwen Tu2Jianlong Qiu3School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, Chongqing, ChinaSchool of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, Chongqing, ChinaSchool of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, Chongqing, ChinaSchool of Automation and Electrical Engineering, Linyi University, Linyi 276005, ChinaIn 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.http://dx.doi.org/10.1155/2020/8526030
collection DOAJ
language English
format Article
sources DOAJ
author Huiling Duan
Tao Peng
Zhengwen Tu
Jianlong Qiu
spellingShingle Huiling Duan
Tao Peng
Zhengwen Tu
Jianlong Qiu
Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays
Complexity
author_facet Huiling Duan
Tao Peng
Zhengwen Tu
Jianlong Qiu
author_sort Huiling Duan
title Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays
title_short Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays
title_full Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays
title_fullStr Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays
title_full_unstemmed Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays
title_sort finite-time stabilization and destabilization analysis of quaternion-valued neural networks with discrete delays
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2020-01-01
description 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.
url http://dx.doi.org/10.1155/2020/8526030
work_keys_str_mv AT huilingduan finitetimestabilizationanddestabilizationanalysisofquaternionvaluedneuralnetworkswithdiscretedelays
AT taopeng finitetimestabilizationanddestabilizationanalysisofquaternionvaluedneuralnetworkswithdiscretedelays
AT zhengwentu finitetimestabilizationanddestabilizationanalysisofquaternionvaluedneuralnetworkswithdiscretedelays
AT jianlongqiu finitetimestabilizationanddestabilizationanalysisofquaternionvaluedneuralnetworkswithdiscretedelays
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