On L ∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control
This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L 2 ([0, 1]) are considered and we...
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| Veröffentlicht in: | ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2020, Vol.26, p.23 |
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| container_title | ESAIM. Control, optimisation and calculus of variations |
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| creator | Dus, Mathias Ferrante, Francesco Prieur, Christophe |
| description | This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in
L
2
([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local
L
∞
exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given. |
| doi_str_mv | 10.1051/cocv/2019069 |
| format | Article |
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L
2
([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local
L
∞
exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.</description><identifier>ISSN: 1292-8119</identifier><identifier>EISSN: 1262-3377</identifier><identifier>DOI: 10.1051/cocv/2019069</identifier><language>eng</language><publisher>Les Ulis: EDP Sciences</publisher><subject>Boundary conditions ; Boundary control ; Feedback control ; Hyperbolic systems ; Partial differential equations ; Stability analysis</subject><ispartof>ESAIM. Control, optimisation and calculus of variations, 2020, Vol.26, p.23</ispartof><rights>2020. This work is licensed under http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2169-c73533e4fac3272f6cff663d09c98719fb1ca6672c93fe4c4f1574d7c6c37be03</citedby><cites>FETCH-LOGICAL-c2169-c73533e4fac3272f6cff663d09c98719fb1ca6672c93fe4c4f1574d7c6c37be03</cites><orcidid>0000-0002-4456-2019</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,4010,27900,27901,27902</link.rule.ids></links><search><creatorcontrib>Dus, Mathias</creatorcontrib><creatorcontrib>Ferrante, Francesco</creatorcontrib><creatorcontrib>Prieur, Christophe</creatorcontrib><title>On L ∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control</title><title>ESAIM. Control, optimisation and calculus of variations</title><description>This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in
L
2
([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local
L
∞
exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.</description><subject>Boundary conditions</subject><subject>Boundary control</subject><subject>Feedback control</subject><subject>Hyperbolic systems</subject><subject>Partial differential equations</subject><subject>Stability analysis</subject><issn>1292-8119</issn><issn>1262-3377</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNotkM9KAzEYxIMoWKs3HyDg1bX5kjRpjlL8B4Ve9OqS_TbRLdtNTbLC-gQ-hQ_nk7jFnmZghmH4EXIJ7AbYHGYY8HPGGRimzBGZAFe8EELr4703vFgAmFNyltKGMVBCygl5XXd0RX-_f2jKtmra5svmJnQ0eFo39i10tqXJbcegczbS92HnYhXaBmkaUnbbRKuBJpv7aLOraRX6rrZxoBi6HEN7Tk68bZO7OOiUvNzfPS8fi9X64Wl5uyqQgzIFajEXwklvUXDNvULvlRI1M2gWGoyvAK1SmqMR3kmUHuZa1hoVCl05Jqbk6n93F8NH71IuN6GP4_lUcrmQXGvOYWxd_7cwhpSi8-UuNtvxbgms3BMs9wTLA0HxB2vhZkg</recordid><startdate>2020</startdate><enddate>2020</enddate><creator>Dus, Mathias</creator><creator>Ferrante, Francesco</creator><creator>Prieur, Christophe</creator><general>EDP Sciences</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-4456-2019</orcidid></search><sort><creationdate>2020</creationdate><title>On L ∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control</title><author>Dus, Mathias ; Ferrante, Francesco ; Prieur, Christophe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2169-c73533e4fac3272f6cff663d09c98719fb1ca6672c93fe4c4f1574d7c6c37be03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Boundary conditions</topic><topic>Boundary control</topic><topic>Feedback control</topic><topic>Hyperbolic systems</topic><topic>Partial differential equations</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dus, Mathias</creatorcontrib><creatorcontrib>Ferrante, Francesco</creatorcontrib><creatorcontrib>Prieur, Christophe</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>ESAIM. Control, optimisation and calculus of variations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dus, Mathias</au><au>Ferrante, Francesco</au><au>Prieur, Christophe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On L ∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control</atitle><jtitle>ESAIM. Control, optimisation and calculus of variations</jtitle><date>2020</date><risdate>2020</risdate><volume>26</volume><spage>23</spage><pages>23-</pages><issn>1292-8119</issn><eissn>1262-3377</eissn><abstract>This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in
L
2
([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local
L
∞
exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.</abstract><cop>Les Ulis</cop><pub>EDP Sciences</pub><doi>10.1051/cocv/2019069</doi><orcidid>https://orcid.org/0000-0002-4456-2019</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | ESAIM. Control, optimisation and calculus of variations, 2020, Vol.26, p.23 |
| issn | 1292-8119 1262-3377 |
| language | eng |
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| source | EZB-FREE-00999 freely available EZB journals |
| subjects | Boundary conditions Boundary control Feedback control Hyperbolic systems Partial differential equations Stability analysis |
| title | On L ∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control |
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