$ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay
This paper investigates $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive neural networks (MNNs) with a non-necessarily differentiable time-varying delay. The objective is to design an output-feedback controller to ensure the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability of the co...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-06-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023588?viewType=HTML |
| _version_ | 1797793959972438016 |
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| author | Jingya Wang Ye Zhu |
| author_facet | Jingya Wang Ye Zhu |
| author_sort | Jingya Wang |
| collection | DOAJ |
| description | This paper investigates $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive neural networks (MNNs) with a non-necessarily differentiable time-varying delay. The objective is to design an output-feedback controller to ensure the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability of the considered MNN. A criterion on the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability is proposed using a Lyapunov functional, the Bessel-Legendre inequality, and the convex combination inequality. Then, a linear matrix inequalities-based design scheme for the required output-feedback controller is developed by decoupling nonlinear terms. Finally, two examples are presented to verify the proposed $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability criterion and design method. |
| first_indexed | 2024-03-13T02:54:49Z |
| format | Article |
| id | doaj.art-b457d83d93bf46e08e9e3226a20a89e6 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-03-13T02:54:49Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-b457d83d93bf46e08e9e3226a20a89e62023-06-28T06:31:10ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-06-01207131821319910.3934/mbe.2023588$ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delayJingya Wang0Ye Zhu1School of Computer Science and Technology, Anhui University of Technology, Ma'anshan 243032, ChinaSchool of Computer Science and Technology, Anhui University of Technology, Ma'anshan 243032, ChinaThis paper investigates $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive neural networks (MNNs) with a non-necessarily differentiable time-varying delay. The objective is to design an output-feedback controller to ensure the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability of the considered MNN. A criterion on the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability is proposed using a Lyapunov functional, the Bessel-Legendre inequality, and the convex combination inequality. Then, a linear matrix inequalities-based design scheme for the required output-feedback controller is developed by decoupling nonlinear terms. Finally, two examples are presented to verify the proposed $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability criterion and design method. https://www.aimspress.com/article/doi/10.3934/mbe.2023588?viewType=HTMLmemristive neural network (mnns)$ \mathcal{l}_{2}-\mathcal{l}_{\infty} $ controlasymptotic stabilitytime-varying delay |
| spellingShingle | Jingya Wang Ye Zhu $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay Mathematical Biosciences and Engineering memristive neural network (mnns) $ \mathcal{l}_{2}-\mathcal{l}_{\infty} $ control asymptotic stability time-varying delay |
| title | $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay |
| title_full | $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay |
| title_fullStr | $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay |
| title_full_unstemmed | $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay |
| title_short | $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay |
| title_sort | mathcal l 2 mathcal l infty control for memristive nns with non necessarily differentiable time varying delay |
| topic | memristive neural network (mnns) $ \mathcal{l}_{2}-\mathcal{l}_{\infty} $ control asymptotic stability time-varying delay |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023588?viewType=HTML |
| work_keys_str_mv | AT jingyawang mathcall2mathcallinftycontrolformemristivennswithnonnecessarilydifferentiabletimevaryingdelay AT yezhu mathcall2mathcallinftycontrolformemristivennswithnonnecessarilydifferentiabletimevaryingdelay |