Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach
In this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2018-06-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13191 |
| _version_ | 1811331266530770944 |
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| author | Zhengwen Tu Jinde Cao Ahmed Alsaedi Bashir Ahmad |
| author_facet | Zhengwen Tu Jinde Cao Ahmed Alsaedi Bashir Ahmad |
| author_sort | Zhengwen Tu |
| collection | DOAJ |
| description | In this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique, some sufficient criteria are derived to ensure the existence and uniqueness of the equilibrium point as well as global stability of delayed QVNNs. In addition, the provided criteria are presented in the form of linear matrix inequality (LMI), which can be easily checked by LMI toolbox in MATLAB. Finally, two simulation examples are demonstrated to verify the effectiveness of obtained results. Moreover, the less conservatism of the obtained results is also showed by two comparison examples. |
| first_indexed | 2024-04-13T16:17:10Z |
| format | Article |
| id | doaj.art-6f15887d79fc4d54a1d78ee73c5a7fef |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-13T16:17:10Z |
| publishDate | 2018-06-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-6f15887d79fc4d54a1d78ee73c5a7fef2022-12-22T02:40:01ZengVilnius University PressNonlinear Analysis1392-51132335-89632018-06-0123310.15388/NA.2018.3.5Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approachZhengwen Tu0Jinde Cao1Ahmed Alsaedi2Bashir Ahmad3Chongqing Three Gorges University, ChinaSoutheast University, China; King Abdulaziz University, Saudi ArabiaKing Abdulaziz UniversityKing Abdulaziz UniversityIn this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique, some sufficient criteria are derived to ensure the existence and uniqueness of the equilibrium point as well as global stability of delayed QVNNs. In addition, the provided criteria are presented in the form of linear matrix inequality (LMI), which can be easily checked by LMI toolbox in MATLAB. Finally, two simulation examples are demonstrated to verify the effectiveness of obtained results. Moreover, the less conservatism of the obtained results is also showed by two comparison examples.http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13191quaternion-valued neural networks (QVNNs)stabilitynonlinear measure approachlinear matrix inequality |
| spellingShingle | Zhengwen Tu Jinde Cao Ahmed Alsaedi Bashir Ahmad Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach Nonlinear Analysis quaternion-valued neural networks (QVNNs) stability nonlinear measure approach linear matrix inequality |
| title | Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach |
| title_full | Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach |
| title_fullStr | Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach |
| title_full_unstemmed | Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach |
| title_short | Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach |
| title_sort | stability analysis for delayed quaternion valued neural networks via nonlinear measure approach |
| topic | quaternion-valued neural networks (QVNNs) stability nonlinear measure approach linear matrix inequality |
| url | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13191 |
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