Stability and stabilization of a class of fractional-order nonlinear systems for \[\varvec{0<}\,{\varvec{\alpha }} \,\varvec{< 2}\]
This paper investigates the stability and stabilization problem of fractional-order nonlinear systems for \[0
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| Veröffentlicht in: | Nonlinear dynamics 2017-04, Vol.88 (2), p.973-984 |
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| container_end_page | 984 |
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| container_issue | 2 |
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| container_title | Nonlinear dynamics |
| container_volume | 88 |
| creator | Huang, Sunhua Wang, Bin |
| description | This paper investigates the stability and stabilization problem of fractional-order nonlinear systems for \[0 |
| doi_str_mv | 10.1007/s11071-016-3288-x |
| format | Article |
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Based on the fractional-order Lyapunov stability theorem, S-procedure and Mittag–Leffler function, the stability conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with \[0<\alpha <2\] are proposed. Finally, typical instances, including the fractional-order nonlinear Chen system and the fractional-order nonlinear Lorenz system, are implemented to demonstrate the feasibility and validity of the proposed method.</description><identifier>ISSN: 0924-090X</identifier><identifier>EISSN: 1573-269X</identifier><identifier>DOI: 10.1007/s11071-016-3288-x</identifier><language>eng</language><publisher>Dordrecht: Springer Nature B.V</publisher><subject>Lorenz system ; Nonlinear systems ; Stability ; Stabilization</subject><ispartof>Nonlinear dynamics, 2017-04, Vol.88 (2), p.973-984</ispartof><rights>Nonlinear Dynamics is a copyright of Springer, (2016). 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Based on the fractional-order Lyapunov stability theorem, S-procedure and Mittag–Leffler function, the stability conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with \[0<\alpha <2\] are proposed. Finally, typical instances, including the fractional-order nonlinear Chen system and the fractional-order nonlinear Lorenz system, are implemented to demonstrate the feasibility and validity of the proposed method.</description><subject>Lorenz system</subject><subject>Nonlinear systems</subject><subject>Stability</subject><subject>Stabilization</subject><issn>0924-090X</issn><issn>1573-269X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNo1j01LAzEURYMoWKs_wF3AbaMvyWQmgW6k-AUFFyoUHCmvkwxOGSc1mRZrmZV_3Jbq6t57FhcOIeccLjlAdhU5h4wz4CmTQmv2dUB6XGWSidRMDkkPjEgYGJgck5MY5wAgBege-XlqcVbVVbum2Fga9-sb28o31JcUaVFjjLtaBix2GGvmg3WBNr6pq8ZhoHEdW_cRaekDzV_zFYaVKzYw7PLB5n_lWC_ekXYdzQf_bEhFl7-dkqMS6-jO_rJPXm5vnkf3bPx49zC6HrMF57JlCkqtADUm2VaxME5pcByUFYh8q6ONLEw240ZwAWJmIU0sCquwlKm1WSH75GL_uwj-c-liO537Zdj6xKkQyiRSJMrIX5HwZJw</recordid><startdate>20170401</startdate><enddate>20170401</enddate><creator>Huang, Sunhua</creator><creator>Wang, Bin</creator><general>Springer Nature B.V</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20170401</creationdate><title>Stability and stabilization of a class of fractional-order nonlinear systems for \[\varvec{0<}\,{\varvec{\alpha }} \,\varvec{< 2}\]</title><author>Huang, Sunhua ; Wang, Bin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p113t-50f850a8a47328c9e580e105d2aa1032893c97b1921202bd064da2d5af36dd7c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Lorenz system</topic><topic>Nonlinear systems</topic><topic>Stability</topic><topic>Stabilization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, Sunhua</creatorcontrib><creatorcontrib>Wang, Bin</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Proquest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Nonlinear dynamics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huang, Sunhua</au><au>Wang, Bin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability and stabilization of a class of fractional-order nonlinear systems for \[\varvec{0<}\,{\varvec{\alpha }} \,\varvec{< 2}\]</atitle><jtitle>Nonlinear dynamics</jtitle><date>2017-04-01</date><risdate>2017</risdate><volume>88</volume><issue>2</issue><spage>973</spage><epage>984</epage><pages>973-984</pages><issn>0924-090X</issn><eissn>1573-269X</eissn><abstract>This paper investigates the stability and stabilization problem of fractional-order nonlinear systems for \[0<\alpha <2\]. Based on the fractional-order Lyapunov stability theorem, S-procedure and Mittag–Leffler function, the stability conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with \[0<\alpha <2\] are proposed. Finally, typical instances, including the fractional-order nonlinear Chen system and the fractional-order nonlinear Lorenz system, are implemented to demonstrate the feasibility and validity of the proposed method.</abstract><cop>Dordrecht</cop><pub>Springer Nature B.V</pub><doi>10.1007/s11071-016-3288-x</doi><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0924-090X |
| ispartof | Nonlinear dynamics, 2017-04, Vol.88 (2), p.973-984 |
| issn | 0924-090X 1573-269X |
| language | eng |
| recordid | cdi_proquest_journals_2259432459 |
| source | SpringerNature Journals |
| subjects | Lorenz system Nonlinear systems Stability Stabilization |
| title | Stability and stabilization of a class of fractional-order nonlinear systems for \[\varvec{0<}\,{\varvec{\alpha }} \,\varvec{< 2}\] |
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