A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks
In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study...
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MDPI AG
2020-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/5/683 |
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| author | Pharunyou Chanthorn Grienggrai Rajchakit Usa Humphries Pramet Kaewmesri Ramalingam Sriraman Chee Peng Lim |
| author_facet | Pharunyou Chanthorn Grienggrai Rajchakit Usa Humphries Pramet Kaewmesri Ramalingam Sriraman Chee Peng Lim |
| author_sort | Pharunyou Chanthorn |
| collection | DOAJ |
| description | In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model. |
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| format | Article |
| id | doaj.art-31e7869098984d92bd316d665f306fb2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:14:15Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
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| series | Symmetry |
| spelling | doaj.art-31e7869098984d92bd316d665f306fb22023-11-19T22:40:47ZengMDPI AGSymmetry2073-89942020-04-0112568310.3390/sym12050683A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural NetworksPharunyou Chanthorn0Grienggrai Rajchakit1Usa Humphries2Pramet Kaewmesri3Ramalingam Sriraman4Chee Peng Lim5Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, ThailandDepartment of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu 600062, IndiaInstitute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, AustraliaIn scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model.https://www.mdpi.com/2073-8994/12/5/683complex-valued Hopfield neural networksrobust stabilityparameter uncertaintiesstochastic effects |
| spellingShingle | Pharunyou Chanthorn Grienggrai Rajchakit Usa Humphries Pramet Kaewmesri Ramalingam Sriraman Chee Peng Lim A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks Symmetry complex-valued Hopfield neural networks robust stability parameter uncertainties stochastic effects |
| title | A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks |
| title_full | A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks |
| title_fullStr | A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks |
| title_full_unstemmed | A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks |
| title_short | A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks |
| title_sort | delay dividing approach to robust stability of uncertain stochastic complex valued hopfield delayed neural networks |
| topic | complex-valued Hopfield neural networks robust stability parameter uncertainties stochastic effects |
| url | https://www.mdpi.com/2073-8994/12/5/683 |
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