Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion
•A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided. This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gr...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2018-04, Vol.57, p.299-308 |
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| container_title | Communications in nonlinear science & numerical simulation |
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| creator | Wu, Guo–Cheng Baleanu, Dumitru Zeng, Sheng–Da |
| description | •A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided.
This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result. |
| doi_str_mv | 10.1016/j.cnsns.2017.09.001 |
| format | Article |
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This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.</description><identifier>ISSN: 1007-5704</identifier><identifier>EISSN: 1878-7274</identifier><identifier>DOI: 10.1016/j.cnsns.2017.09.001</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Difference equations ; Differential equations ; Discrete element method ; Discrete time control ; Finite-time stability ; Fractional difference equations ; Image processing systems ; Mathematical analysis ; Stability criteria ; Time scale</subject><ispartof>Communications in nonlinear science & numerical simulation, 2018-04, Vol.57, p.299-308</ispartof><rights>2017 Elsevier B.V.</rights><rights>Copyright Elsevier Science Ltd. Apr 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-2fcd608280f8c316d5c0520d69c2d988225d30b4d028f4d7211632f32eca96ad3</citedby><cites>FETCH-LOGICAL-c331t-2fcd608280f8c316d5c0520d69c2d988225d30b4d028f4d7211632f32eca96ad3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cnsns.2017.09.001$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids></links><search><creatorcontrib>Wu, Guo–Cheng</creatorcontrib><creatorcontrib>Baleanu, Dumitru</creatorcontrib><creatorcontrib>Zeng, Sheng–Da</creatorcontrib><title>Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion</title><title>Communications in nonlinear science & numerical simulation</title><description>•A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided.
This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.</description><subject>Difference equations</subject><subject>Differential equations</subject><subject>Discrete element method</subject><subject>Discrete time control</subject><subject>Finite-time stability</subject><subject>Fractional difference equations</subject><subject>Image processing systems</subject><subject>Mathematical analysis</subject><subject>Stability criteria</subject><subject>Time scale</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKu_wEvA866TZD-yggcptgoFL3oOaT4kyzbbJqnSf2_aevDkaebwPi8zD0K3BEoCpLnvS-WjjyUF0pbQlQDkDE0Ib3nR0rY6zztAW9QtVJfoKsY-B5quriboc-68S6ZIbm1wTHLlBpf2eLRYu6iCSQbbIFVyo5cD1maQexz3MZl1fMCLMPpvOQzYebPdySMpvf7To0IuDxm-RhdWDtHc_M4p-pg_v89eiuXb4nX2tCwUYyQV1CrdAKccLFeMNLpWUFPQTaeo7jintNYMVpUGym2lW0pIw6hl1CjZNVKzKbo79W7CuN2ZmEQ_7kK-PQoKtOIANaM5xU4pFcYYg7FiE9xahr0gIA5GRS-ORsXBqIBOZGGZejxRJj_w5UwQUTnjldEuGJWEHt2__A9Qg4GJ</recordid><startdate>201804</startdate><enddate>201804</enddate><creator>Wu, Guo–Cheng</creator><creator>Baleanu, Dumitru</creator><creator>Zeng, Sheng–Da</creator><general>Elsevier B.V</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201804</creationdate><title>Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion</title><author>Wu, Guo–Cheng ; Baleanu, Dumitru ; Zeng, Sheng–Da</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-2fcd608280f8c316d5c0520d69c2d988225d30b4d028f4d7211632f32eca96ad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Difference equations</topic><topic>Differential equations</topic><topic>Discrete element method</topic><topic>Discrete time control</topic><topic>Finite-time stability</topic><topic>Fractional difference equations</topic><topic>Image processing systems</topic><topic>Mathematical analysis</topic><topic>Stability criteria</topic><topic>Time scale</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Guo–Cheng</creatorcontrib><creatorcontrib>Baleanu, Dumitru</creatorcontrib><creatorcontrib>Zeng, Sheng–Da</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wu, Guo–Cheng</au><au>Baleanu, Dumitru</au><au>Zeng, Sheng–Da</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2018-04</date><risdate>2018</risdate><volume>57</volume><spage>299</spage><epage>308</epage><pages>299-308</pages><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>•A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided.
This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cnsns.2017.09.001</doi><tpages>10</tpages></addata></record> |
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| ispartof | Communications in nonlinear science & numerical simulation, 2018-04, Vol.57, p.299-308 |
| issn | 1007-5704 1878-7274 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Difference equations Differential equations Discrete element method Discrete time control Finite-time stability Fractional difference equations Image processing systems Mathematical analysis Stability criteria Time scale |
| title | Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion |
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