Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method
At present, the theory and application of fractional-order neural networks remain in the exploratory stage. We study the asymptotic stability of fractional-order neural networks with Riemann-Liouville (R-L) derivatives. For non-delayed and delayed systems, we propose an asymptotic stability criterio...
| Үндсэн зохиолчид: | , , , |
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| Формат: | Өгүүллэг |
| Хэл сонгох: | English |
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IEEE
2021-01-01
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| Цуврал: | IEEE Access |
| Нөхцлүүд: | |
| Онлайн хандалт: | https://ieeexplore.ieee.org/document/9530518/ |
| _version_ | 1831536146234998784 |
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| author | Xin Chang Qinkun Xiao Yilin Zhu Jielei Xiao |
| author_facet | Xin Chang Qinkun Xiao Yilin Zhu Jielei Xiao |
| author_sort | Xin Chang |
| collection | DOAJ |
| description | At present, the theory and application of fractional-order neural networks remain in the exploratory stage. We study the asymptotic stability of fractional-order neural networks with Riemann-Liouville (R-L) derivatives. For non-delayed and delayed systems, we propose an asymptotic stability criterion based on the combination of the Lyapunov method and linear matrix inequality (LMI) method. The highlights include the following: (1) for fractional-order neural networks with time delay, the existence and uniqueness of solutions are proven by using matrix analysis theory and contraction mapping theorem, and (2) based on the unique solution, a suitable Lyapunov functional is constructed. Based on the inequality theorem and LMI method, two sets of asymptotic stability criteria for fractional-order neural networks are proven, which avoids the difficulty of solving the fractional derivative by the Leibniz law. Finally, the results are verified using numerical simulations. |
| first_indexed | 2024-12-16T22:45:34Z |
| format | Article |
| id | doaj.art-dfc9ed664c2049c5b5eeb39bec75e47d |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T22:45:34Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-dfc9ed664c2049c5b5eeb39bec75e47d2022-12-21T22:13:14ZengIEEEIEEE Access2169-35362021-01-01912413212414110.1109/ACCESS.2021.31107649530518Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov MethodXin Chang0https://orcid.org/0000-0001-9558-8422Qinkun Xiao1https://orcid.org/0000-0002-2651-1218Yilin Zhu2https://orcid.org/0000-0002-5704-4501Jielei Xiao3https://orcid.org/0000-0002-7592-6268Department of Electronics Information and Engineering, Xi’an Technological University, Xi’an, ChinaDepartment of Electronics Information and Engineering, Xi’an Technological University, Xi’an, ChinaDepartment of Electronics Information and Engineering, Xi’an Technological University, Xi’an, ChinaSenior High School, Xi’an Tieyi Middle School, Xi’an, ChinaAt present, the theory and application of fractional-order neural networks remain in the exploratory stage. We study the asymptotic stability of fractional-order neural networks with Riemann-Liouville (R-L) derivatives. For non-delayed and delayed systems, we propose an asymptotic stability criterion based on the combination of the Lyapunov method and linear matrix inequality (LMI) method. The highlights include the following: (1) for fractional-order neural networks with time delay, the existence and uniqueness of solutions are proven by using matrix analysis theory and contraction mapping theorem, and (2) based on the unique solution, a suitable Lyapunov functional is constructed. Based on the inequality theorem and LMI method, two sets of asymptotic stability criteria for fractional-order neural networks are proven, which avoids the difficulty of solving the fractional derivative by the Leibniz law. Finally, the results are verified using numerical simulations.https://ieeexplore.ieee.org/document/9530518/Fractional-order neural networkstime delayasymptotic stabilityLyapunovLMI |
| spellingShingle | Xin Chang Qinkun Xiao Yilin Zhu Jielei Xiao Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method IEEE Access Fractional-order neural networks time delay asymptotic stability Lyapunov LMI |
| title | Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method |
| title_full | Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method |
| title_fullStr | Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method |
| title_full_unstemmed | Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method |
| title_short | Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method |
| title_sort | stability analysis of two kinds of fractional order neural networks based on lyapunov method |
| topic | Fractional-order neural networks time delay asymptotic stability Lyapunov LMI |
| url | https://ieeexplore.ieee.org/document/9530518/ |
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