Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks
Abstract This paper deals with the global Mittag-Leffler synchronization of fractional-order memristive neural networks (FMNNs) with time delay. Since the FMNNs are essentially a class of switched systems with irregular switching laws, it is more difficult to achieve synchronization than with the tr...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1800-y |
| _version_ | 1818439549246767104 |
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| author | Yingjie Fan Xia Huang Zhen Wang Jianwei Xia Yuxia Li |
| author_facet | Yingjie Fan Xia Huang Zhen Wang Jianwei Xia Yuxia Li |
| author_sort | Yingjie Fan |
| collection | DOAJ |
| description | Abstract This paper deals with the global Mittag-Leffler synchronization of fractional-order memristive neural networks (FMNNs) with time delay. Since the FMNNs are essentially a class of switched systems with irregular switching laws, it is more difficult to achieve synchronization than with the traditional neural networks. First, under the framework of fractional-order differential inclusions and set-valued maps, the FMNNs are transformed into a continuous system with uncertainties. Then a linear state feedback combined with switching control law is designed in order to achieve the Mittag-Leffler synchronization. In addition, several synchronization criteria are obtained by constructing appropriate Lyapunov functionals, together with the help of some inequality techniques. Finally, an example is given to demonstrate the effectiveness of the obtained results. |
| first_indexed | 2024-12-14T17:58:14Z |
| format | Article |
| id | doaj.art-42c844e3406e4eabac0fc5bb5a3f002d |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T17:58:14Z |
| publishDate | 2018-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-42c844e3406e4eabac0fc5bb5a3f002d2022-12-21T22:52:30ZengSpringerOpenAdvances in Difference Equations1687-18472018-09-012018111510.1186/s13662-018-1800-yGlobal Mittag-Leffler synchronization of delayed fractional-order memristive neural networksYingjie Fan0Xia Huang1Zhen Wang2Jianwei Xia3Yuxia Li4College of Electrical Engineering and Automation, Shandong University of Science and TechnologyCollege of Electrical Engineering and Automation, Shandong University of Science and TechnologyCollege of Mathematics and Systems Science, Shandong University of Science and TechnologySchool of Mathematic Science, Liaocheng UniversityCollege of Electrical Engineering and Automation, Shandong University of Science and TechnologyAbstract This paper deals with the global Mittag-Leffler synchronization of fractional-order memristive neural networks (FMNNs) with time delay. Since the FMNNs are essentially a class of switched systems with irregular switching laws, it is more difficult to achieve synchronization than with the traditional neural networks. First, under the framework of fractional-order differential inclusions and set-valued maps, the FMNNs are transformed into a continuous system with uncertainties. Then a linear state feedback combined with switching control law is designed in order to achieve the Mittag-Leffler synchronization. In addition, several synchronization criteria are obtained by constructing appropriate Lyapunov functionals, together with the help of some inequality techniques. Finally, an example is given to demonstrate the effectiveness of the obtained results.http://link.springer.com/article/10.1186/s13662-018-1800-yMittag-Leffler synchronizationFractional-order systemsMemristive neural networksState feedback controlSwitching control |
| spellingShingle | Yingjie Fan Xia Huang Zhen Wang Jianwei Xia Yuxia Li Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks Advances in Difference Equations Mittag-Leffler synchronization Fractional-order systems Memristive neural networks State feedback control Switching control |
| title | Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks |
| title_full | Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks |
| title_fullStr | Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks |
| title_full_unstemmed | Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks |
| title_short | Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks |
| title_sort | global mittag leffler synchronization of delayed fractional order memristive neural networks |
| topic | Mittag-Leffler synchronization Fractional-order systems Memristive neural networks State feedback control Switching control |
| url | http://link.springer.com/article/10.1186/s13662-018-1800-y |
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