Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method.
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| Title: | Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method. |
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| Authors: | Wang, Chen-Rui1,2 (AUTHOR) wangcr@cug.edu.cn, He, Yong1,2 (AUTHOR) heyong08@cug.edu.cn, Lin, Wen-Juan1,2 (AUTHOR) linwenjuan@cug.edu.cn |
| Source: | Applied Mathematics & Computation. Feb2021, Vol. 391, pN.PAG-N.PAG. 1p. |
| Subjects: | Stability criterion, Conservatism, Problem solving |
| Abstract: | • An improved Lyapunov-Krasovskii functional (LKF) is proposed by considering more key information about delay states, integral terms and the activation function and can get a less conservative stability criterion. • A new relaxed quadratic function negative-determination provides a valid way to deal with the problem of the negative quadratic function. The generalized reciprocally convex combination is been used to solve the problem of the delay function τ ˙ (t) in the denominator. Combining the novel augmented LKF itself and its derivative with both of the above methods, a new less conservative stability criterion is obtained. • In addition, the difference with the previous researches is that the MADBs are obtained by the stability condition with the value of the delay τ (t) bound information rather than using the value of its derivative. It is worth noting that the criterion removes the derivative constraint of time-varying delay, which means fast-varying delay is allowed. • Some numerical examples are presented to prove the effectiveness and lower conservatism of the new stability criterion. This paper studies the problem of stability analysis of generalized neural networks (GNN) with a fast-varying delay. Firstly, an improved augmented Lyapunov-Krasovskii functional (LKF) is proposed by fully considering more states information about interrelated systems and neuron activation function conditions. Then, to handle the derivative of the LKF, the generalized reciprocally convex combination and a relaxed quadratic function negative-determination are employed. Based on these methods and the augmented LKF, a less conservative delay-dependent stability criterion for GNN with a fast-varying delay is presented. Finally, some numerical examples are given to demonstrate the effective superiority of the proposed criterion. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Computation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 147071101 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wang%2C+Chen-Rui%22">Wang, Chen-Rui</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> wangcr@cug.edu.cn</i><br /><searchLink fieldCode="AR" term="%22He%2C+Yong%22">He, Yong</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> heyong08@cug.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lin%2C+Wen-Juan%22">Lin, Wen-Juan</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> linwenjuan@cug.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Computation%22">Applied Mathematics & Computation</searchLink>. Feb2021, Vol. 391, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Stability+criterion%22">Stability criterion</searchLink><br /><searchLink fieldCode="DE" term="%22Conservatism%22">Conservatism</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+solving%22">Problem solving</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: • An improved Lyapunov-Krasovskii functional (LKF) is proposed by considering more key information about delay states, integral terms and the activation function and can get a less conservative stability criterion. • A new relaxed quadratic function negative-determination provides a valid way to deal with the problem of the negative quadratic function. The generalized reciprocally convex combination is been used to solve the problem of the delay function τ ˙ (t) in the denominator. Combining the novel augmented LKF itself and its derivative with both of the above methods, a new less conservative stability criterion is obtained. • In addition, the difference with the previous researches is that the MADBs are obtained by the stability condition with the value of the delay τ (t) bound information rather than using the value of its derivative. It is worth noting that the criterion removes the derivative constraint of time-varying delay, which means fast-varying delay is allowed. • Some numerical examples are presented to prove the effectiveness and lower conservatism of the new stability criterion. This paper studies the problem of stability analysis of generalized neural networks (GNN) with a fast-varying delay. Firstly, an improved augmented Lyapunov-Krasovskii functional (LKF) is proposed by fully considering more states information about interrelated systems and neuron activation function conditions. Then, to handle the derivative of the LKF, the generalized reciprocally convex combination and a relaxed quadratic function negative-determination are employed. Based on these methods and the augmented LKF, a less conservative delay-dependent stability criterion for GNN with a fast-varying delay is presented. Finally, some numerical examples are given to demonstrate the effective superiority of the proposed criterion. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Computation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.amc.2020.125631 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Stability criterion Type: general – SubjectFull: Conservatism Type: general – SubjectFull: Problem solving Type: general Titles: – TitleFull: Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wang, Chen-Rui – PersonEntity: Name: NameFull: He, Yong – PersonEntity: Name: NameFull: Lin, Wen-Juan IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 02 Text: Feb2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 00963003 Numbering: – Type: volume Value: 391 Titles: – TitleFull: Applied Mathematics & Computation Type: main |
| ResultId | 1 |
