Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases
Identifieur interne : 004397 ( Main/Merge ); précédent : 004396; suivant : 004398Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases
Auteurs : Antoine Chaillet [France] ; Yacine Chitour [France] ; Antonio Loría [France] ; Mario Sigalotti [France]Source :
- Mathematics of Control, Signals, and Systems [ 0932-4194 ] ; 2008-06-01.
English descriptors
- KwdEn :
- mix :
Abstract
Abstract: Consider the controlled system dx/dt = Ax + α(t)Bu where the pair (A, B) is stabilizable and α(t) takes values in [0, 1] and is persistently exciting, i.e., there exist two positive constants μ, T such that, for every t ≥ 0, $${\int_t^{t+T}\alpha(s){\rm d}s \geq \mu}$$ . In particular, when α(t) becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback u = Kx, with K only depending on (A, B) and possibly on μ, T, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when A is neutrally stable and when the system is the double integrator.
Url:
- https://api.istex.fr/ark:/67375/VQC-G1CGZ3CS-F/fulltext.pdf
- https://hal.archives-ouvertes.fr/hal-00132968
DOI: 10.1007/s00498-008-0024-1
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 003702
- to stream Istex, to step Curation: 003660
- to stream Istex, to step Checkpoint: 000D14
- to stream Hal, to step Corpus: 005064
- to stream Hal, to step Curation: 005064
- to stream Hal, to step Checkpoint: 003524
Links to Exploration step
ISTEX:E5228823767CC6FDD6407DC4086EC5CC2B978A1CLe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases</title><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name></author><author><name sortKey="Chitour, Yacine" sort="Chitour, Yacine" uniqKey="Chitour Y" first="Yacine" last="Chitour">Yacine Chitour</name></author><author><name sortKey="Loria, Antonio" sort="Loria, Antonio" uniqKey="Loria A" first="Antonio" last="Loría">Antonio Loría</name></author><author><name sortKey="Sigalotti, Mario" sort="Sigalotti, Mario" uniqKey="Sigalotti M" first="Mario" last="Sigalotti">Mario Sigalotti</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:E5228823767CC6FDD6407DC4086EC5CC2B978A1C</idno><date when="2008" year="2008">2008</date><idno type="doi">10.1007/s00498-008-0024-1</idno><idno type="url">https://api.istex.fr/ark:/67375/VQC-G1CGZ3CS-F/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">003702</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">003702</idno><idno type="wicri:Area/Istex/Curation">003660</idno><idno type="wicri:Area/Istex/Checkpoint">000D14</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000D14</idno><idno type="wicri:doubleKey">0932-4194:2008:Chaillet A:uniform:stabilization:for</idno><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:hal-00132968</idno><idno type="url">https://hal.archives-ouvertes.fr/hal-00132968</idno><idno type="wicri:Area/Hal/Corpus">005064</idno><idno type="wicri:Area/Hal/Curation">005064</idno><idno type="wicri:Area/Hal/Checkpoint">003524</idno><idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">003524</idno><idno type="wicri:doubleKey">0932-4194:2008:Chaillet A:uniform:stabilization:for</idno><idno type="wicri:Area/Main/Merge">004397</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases</title><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire des Signaux et Systèmes, Supélec, 3, Rue Joliot Curie, 91192, Gif s/Yvette</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Gif s/Yvette</settlement></placeName></affiliation><affiliation wicri:level="4"><country xml:lang="fr">France</country><wicri:regionArea>Université Paris Sud, Orsay</wicri:regionArea><placeName><settlement type="city">Orsay</settlement></placeName><orgName type="university">Université Paris-Sud</orgName></affiliation><affiliation></affiliation></author><author><name sortKey="Chitour, Yacine" sort="Chitour, Yacine" uniqKey="Chitour Y" first="Yacine" last="Chitour">Yacine Chitour</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire des Signaux et Systèmes, Supélec, 3, Rue Joliot Curie, 91192, Gif s/Yvette</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Gif s/Yvette</settlement></placeName></affiliation><affiliation wicri:level="4"><country xml:lang="fr">France</country><wicri:regionArea>Université Paris Sud, Orsay</wicri:regionArea><placeName><settlement type="city">Orsay</settlement></placeName><orgName type="university">Université Paris-Sud</orgName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Loria, Antonio" sort="Loria, Antonio" uniqKey="Loria A" first="Antonio" last="Loría">Antonio Loría</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire des Signaux et Systèmes, Supélec, 3, Rue Joliot Curie, 91192, Gif s/Yvette</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Gif s/Yvette</settlement></placeName></affiliation><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>C.N.R.S., 54506, Vandœuvre-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Sigalotti, Mario" sort="Sigalotti, Mario" uniqKey="Sigalotti M" first="Mario" last="Sigalotti">Mario Sigalotti</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>INRIA, Institut Élie Cartan, UMR 7502 Nancy-Université/CNRS/INRIA, POB 239, 54506, Vandœuvre-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Mathematics of Control, Signals, and Systems</title><title level="j" type="abbrev">Math. Control Signals Syst.</title><idno type="ISSN">0932-4194</idno><idno type="eISSN">1435-568X</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>London</pubPlace><date type="published" when="2008-06-01">2008-06-01</date><biblScope unit="volume">20</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="135">135</biblScope><biblScope unit="page" to="156">156</biblScope></imprint><idno type="ISSN">0932-4194</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0932-4194</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Persistency of excitation</term><term>Stabilization</term><term>Switching systems</term><term>Time-varying linear systems</term></keywords><keywords scheme="mix" xml:lang="en"><term>permanent excitation</term><term>switching system</term><term>uniform stability</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Consider the controlled system dx/dt = Ax + α(t)Bu where the pair (A, B) is stabilizable and α(t) takes values in [0, 1] and is persistently exciting, i.e., there exist two positive constants μ, T such that, for every t ≥ 0, $${\int_t^{t+T}\alpha(s){\rm d}s \geq \mu}$$ . In particular, when α(t) becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback u = Kx, with K only depending on (A, B) and possibly on μ, T, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when A is neutrally stable and when the system is the double integrator.</div></front></TEI><double doi="10.1007/s00498-008-0024-1"><HAL><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases</title><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-30081" status="INCOMING"><orgName>Interdepartemental Research Center "E. Piaggio"</orgName><desc><address><country key="IT"></country></address></desc><listRelation><relation active="#struct-301339" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-301339" type="direct"><org type="institution" xml:id="struct-301339" status="VALID"><orgName>Università di Pisa</orgName><desc><address><addrLine>Università di PisaLungarno Pacinotti 4356126 Pisa</addrLine><country key="IT"></country></address><ref type="url">https://www.unipi.it/index.php/english</ref></desc></org></tutelle></tutelles></hal:affiliation><country>Italie</country><placeName><settlement type="city">Pise</settlement><region type="region" nuts="2">Toscane</region></placeName><orgName type="university">Université de Pise</orgName></affiliation></author><author><name sortKey="Chitour, Yacine" sort="Chitour, Yacine" uniqKey="Chitour Y" first="Yacine" last="Chitour">Yacine Chitour</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-1289" status="VALID"><idno type="RNSR">199812842X</idno><orgName>Laboratoire des signaux et systèmes</orgName><orgName type="acronym">L2S</orgName><desc><address><addrLine>Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://www.lss.supelec.fr/</ref></desc><listRelation><relation active="#struct-411575" type="direct"></relation><relation active="#struct-92966" type="direct"></relation><relation active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-411575" type="direct"><org type="institution" xml:id="struct-411575" status="VALID"><orgName>CentraleSupélec</orgName><desc><address><addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.centralesupelec.fr</ref></desc></org></tutelle><tutelle active="#struct-92966" type="direct"><org type="institution" xml:id="struct-92966" status="VALID"><orgName>Université Paris-Sud - Paris 11</orgName><orgName type="acronym">UP11</orgName><desc><address><addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-psud.fr/</ref></desc></org></tutelle><tutelle active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Loria, Antonio" sort="Loria, Antonio" uniqKey="Loria A" first="Antonio" last="Loría">Antonio Loría</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-1289" status="VALID"><idno type="RNSR">199812842X</idno><orgName>Laboratoire des signaux et systèmes</orgName><orgName type="acronym">L2S</orgName><desc><address><addrLine>Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://www.lss.supelec.fr/</ref></desc><listRelation><relation active="#struct-411575" type="direct"></relation><relation active="#struct-92966" type="direct"></relation><relation active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-411575" type="direct"><org type="institution" xml:id="struct-411575" status="VALID"><orgName>CentraleSupélec</orgName><desc><address><addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.centralesupelec.fr</ref></desc></org></tutelle><tutelle active="#struct-92966" type="direct"><org type="institution" xml:id="struct-92966" status="VALID"><orgName>Université Paris-Sud - Paris 11</orgName><orgName type="acronym">UP11</orgName><desc><address><addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-psud.fr/</ref></desc></org></tutelle><tutelle active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Sigalotti, Mario" sort="Sigalotti, Mario" uniqKey="Sigalotti M" first="Mario" last="Sigalotti">Mario Sigalotti</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2368" status="OLD"><idno type="RNSR">200218300M</idno><orgName>Robust control of infinite dimensional systems and applications</orgName><orgName type="acronym">CORIDA</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/corida</ref></desc><listRelation><relation active="#struct-23" type="direct"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation name="UMR7502" active="#struct-441569" type="indirect"></relation><relation active="#struct-115885" type="direct"></relation><relation active="#struct-300289" type="indirect"></relation><relation name="UMR7122" active="#struct-441569" type="indirect"></relation><relation active="#struct-129671" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-23" type="direct"><org type="laboratory" xml:id="struct-23" status="OLD"><orgName>Institut Élie Cartan de Nancy</orgName><orgName type="acronym">IECN</orgName><date type="end">2012-12-31</date><desc><address><addrLine>Université Henri Poincaré, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.iecn.u-nancy.fr/</ref></desc><listRelation><relation active="#struct-300293" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation name="UMR7502" active="#struct-441569" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle name="UMR7502" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-115885" type="direct"><org type="laboratory" xml:id="struct-115885" status="OLD"><orgName>Laboratoire de Mathématiques et Applications de Metz</orgName><orgName type="acronym">LMAM</orgName><date type="end">2012-12-31</date><desc><address><addrLine>Université Paul Verlaine - Metz, Bât. A, Ile du Saulcy F-57045 METZ Cedex 1 FRANCE</addrLine><country key="FR"></country></address><ref type="url">http://www.math.univ-metz.fr</ref></desc><listRelation><relation active="#struct-300289" type="direct"></relation><relation name="UMR7122" active="#struct-441569" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-300289" type="indirect"><org type="institution" xml:id="struct-300289" status="OLD"><orgName>Université Paul Verlaine - Metz</orgName><orgName type="acronym">UPVM</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle name="UMR7122" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno><orgName>INRIA Nancy - Grand Est</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/nancy</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Metz</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Paul Verlaine - Metz</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:hal-00132968</idno><idno type="halId">hal-00132968</idno><idno type="halUri">https://hal.archives-ouvertes.fr/hal-00132968</idno><idno type="url">https://hal.archives-ouvertes.fr/hal-00132968</idno><idno type="doi">10.1007/s00498-008-0024-1</idno><date when="2008">2008</date><idno type="wicri:Area/Hal/Corpus">005064</idno><idno type="wicri:Area/Hal/Curation">005064</idno><idno type="wicri:Area/Hal/Checkpoint">003524</idno><idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">003524</idno><idno type="wicri:doubleKey">0932-4194:2008:Chaillet A:uniform:stabilization:for</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases</title><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-30081" status="INCOMING"><orgName>Interdepartemental Research Center "E. Piaggio"</orgName><desc><address><country key="IT"></country></address></desc><listRelation><relation active="#struct-301339" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-301339" type="direct"><org type="institution" xml:id="struct-301339" status="VALID"><orgName>Università di Pisa</orgName><desc><address><addrLine>Università di PisaLungarno Pacinotti 4356126 Pisa</addrLine><country key="IT"></country></address><ref type="url">https://www.unipi.it/index.php/english</ref></desc></org></tutelle></tutelles></hal:affiliation><country>Italie</country><placeName><settlement type="city">Pise</settlement><region type="region" nuts="2">Toscane</region></placeName><orgName type="university">Université de Pise</orgName></affiliation></author><author><name sortKey="Chitour, Yacine" sort="Chitour, Yacine" uniqKey="Chitour Y" first="Yacine" last="Chitour">Yacine Chitour</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-1289" status="VALID"><idno type="RNSR">199812842X</idno><orgName>Laboratoire des signaux et systèmes</orgName><orgName type="acronym">L2S</orgName><desc><address><addrLine>Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://www.lss.supelec.fr/</ref></desc><listRelation><relation active="#struct-411575" type="direct"></relation><relation active="#struct-92966" type="direct"></relation><relation active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-411575" type="direct"><org type="institution" xml:id="struct-411575" status="VALID"><orgName>CentraleSupélec</orgName><desc><address><addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.centralesupelec.fr</ref></desc></org></tutelle><tutelle active="#struct-92966" type="direct"><org type="institution" xml:id="struct-92966" status="VALID"><orgName>Université Paris-Sud - Paris 11</orgName><orgName type="acronym">UP11</orgName><desc><address><addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-psud.fr/</ref></desc></org></tutelle><tutelle active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Loria, Antonio" sort="Loria, Antonio" uniqKey="Loria A" first="Antonio" last="Loría">Antonio Loría</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-1289" status="VALID"><idno type="RNSR">199812842X</idno><orgName>Laboratoire des signaux et systèmes</orgName><orgName type="acronym">L2S</orgName><desc><address><addrLine>Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://www.lss.supelec.fr/</ref></desc><listRelation><relation active="#struct-411575" type="direct"></relation><relation active="#struct-92966" type="direct"></relation><relation active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-411575" type="direct"><org type="institution" xml:id="struct-411575" status="VALID"><orgName>CentraleSupélec</orgName><desc><address><addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.centralesupelec.fr</ref></desc></org></tutelle><tutelle active="#struct-92966" type="direct"><org type="institution" xml:id="struct-92966" status="VALID"><orgName>Université Paris-Sud - Paris 11</orgName><orgName type="acronym">UP11</orgName><desc><address><addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-psud.fr/</ref></desc></org></tutelle><tutelle active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Sigalotti, Mario" sort="Sigalotti, Mario" uniqKey="Sigalotti M" first="Mario" last="Sigalotti">Mario Sigalotti</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2368" status="OLD"><idno type="RNSR">200218300M</idno><orgName>Robust control of infinite dimensional systems and applications</orgName><orgName type="acronym">CORIDA</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/corida</ref></desc><listRelation><relation active="#struct-23" type="direct"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation name="UMR7502" active="#struct-441569" type="indirect"></relation><relation active="#struct-115885" type="direct"></relation><relation active="#struct-300289" type="indirect"></relation><relation name="UMR7122" active="#struct-441569" type="indirect"></relation><relation active="#struct-129671" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-23" type="direct"><org type="laboratory" xml:id="struct-23" status="OLD"><orgName>Institut Élie Cartan de Nancy</orgName><orgName type="acronym">IECN</orgName><date type="end">2012-12-31</date><desc><address><addrLine>Université Henri Poincaré, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.iecn.u-nancy.fr/</ref></desc><listRelation><relation active="#struct-300293" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation name="UMR7502" active="#struct-441569" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle name="UMR7502" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-115885" type="direct"><org type="laboratory" xml:id="struct-115885" status="OLD"><orgName>Laboratoire de Mathématiques et Applications de Metz</orgName><orgName type="acronym">LMAM</orgName><date type="end">2012-12-31</date><desc><address><addrLine>Université Paul Verlaine - Metz, Bât. A, Ile du Saulcy F-57045 METZ Cedex 1 FRANCE</addrLine><country key="FR"></country></address><ref type="url">http://www.math.univ-metz.fr</ref></desc><listRelation><relation active="#struct-300289" type="direct"></relation><relation name="UMR7122" active="#struct-441569" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-300289" type="indirect"><org type="institution" xml:id="struct-300289" status="OLD"><orgName>Université Paul Verlaine - Metz</orgName><orgName type="acronym">UPVM</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle name="UMR7122" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno><orgName>INRIA Nancy - Grand Est</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/nancy</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Metz</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Paul Verlaine - Metz</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic><idno type="DOI">10.1007/s00498-008-0024-1</idno><series><title level="j">Mathematics of Control, Signals, and Systems</title><idno type="ISSN">0932-4194</idno><imprint><date type="datePub">2008</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>permanent excitation</term><term>switching system</term><term>uniform stability</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\mu,T$ such that, for every $t\geq 0$, $\int_t^{t+T}\alpha(s)ds\geq \mu$. In particular, when $\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback $u=Kx$, with $K$ only depending on $(A,B)$ and possibly on $\mu,T$, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when $A$ is neutrally stable and when the system is the double integrator.</div></front></TEI></HAL><ISTEX><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases</title><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name></author><author><name sortKey="Chitour, Yacine" sort="Chitour, Yacine" uniqKey="Chitour Y" first="Yacine" last="Chitour">Yacine Chitour</name></author><author><name sortKey="Loria, Antonio" sort="Loria, Antonio" uniqKey="Loria A" first="Antonio" last="Loría">Antonio Loría</name></author><author><name sortKey="Sigalotti, Mario" sort="Sigalotti, Mario" uniqKey="Sigalotti M" first="Mario" last="Sigalotti">Mario Sigalotti</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:E5228823767CC6FDD6407DC4086EC5CC2B978A1C</idno><date when="2008" year="2008">2008</date><idno type="doi">10.1007/s00498-008-0024-1</idno><idno type="url">https://api.istex.fr/ark:/67375/VQC-G1CGZ3CS-F/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">003702</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">003702</idno><idno type="wicri:Area/Istex/Curation">003660</idno><idno type="wicri:Area/Istex/Checkpoint">000D14</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000D14</idno><idno type="wicri:doubleKey">0932-4194:2008:Chaillet A:uniform:stabilization:for</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases</title><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire des Signaux et Systèmes, Supélec, 3, Rue Joliot Curie, 91192, Gif s/Yvette</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Gif s/Yvette</settlement></placeName></affiliation><affiliation wicri:level="4"><country xml:lang="fr">France</country><wicri:regionArea>Université Paris Sud, Orsay</wicri:regionArea><placeName><settlement type="city">Orsay</settlement></placeName><orgName type="university">Université Paris-Sud</orgName></affiliation><affiliation></affiliation></author><author><name sortKey="Chitour, Yacine" sort="Chitour, Yacine" uniqKey="Chitour Y" first="Yacine" last="Chitour">Yacine Chitour</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire des Signaux et Systèmes, Supélec, 3, Rue Joliot Curie, 91192, Gif s/Yvette</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Gif s/Yvette</settlement></placeName></affiliation><affiliation wicri:level="4"><country xml:lang="fr">France</country><wicri:regionArea>Université Paris Sud, Orsay</wicri:regionArea><placeName><settlement type="city">Orsay</settlement></placeName><orgName type="university">Université Paris-Sud</orgName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Loria, Antonio" sort="Loria, Antonio" uniqKey="Loria A" first="Antonio" last="Loría">Antonio Loría</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire des Signaux et Systèmes, Supélec, 3, Rue Joliot Curie, 91192, Gif s/Yvette</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Gif s/Yvette</settlement></placeName></affiliation><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>C.N.R.S., 54506, Vandœuvre-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Sigalotti, Mario" sort="Sigalotti, Mario" uniqKey="Sigalotti M" first="Mario" last="Sigalotti">Mario Sigalotti</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>INRIA, Institut Élie Cartan, UMR 7502 Nancy-Université/CNRS/INRIA, POB 239, 54506, Vandœuvre-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Mathematics of Control, Signals, and Systems</title><title level="j" type="abbrev">Math. Control Signals Syst.</title><idno type="ISSN">0932-4194</idno><idno type="eISSN">1435-568X</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>London</pubPlace><date type="published" when="2008-06-01">2008-06-01</date><biblScope unit="volume">20</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="135">135</biblScope><biblScope unit="page" to="156">156</biblScope></imprint><idno type="ISSN">0932-4194</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0932-4194</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Persistency of excitation</term><term>Stabilization</term><term>Switching systems</term><term>Time-varying linear systems</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Consider the controlled system dx/dt = Ax + α(t)Bu where the pair (A, B) is stabilizable and α(t) takes values in [0, 1] and is persistently exciting, i.e., there exist two positive constants μ, T such that, for every t ≥ 0, $${\int_t^{t+T}\alpha(s){\rm d}s \geq \mu}$$ . In particular, when α(t) becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback u = Kx, with K only depending on (A, B) and possibly on μ, T, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when A is neutrally stable and when the system is the double integrator.</div></front></TEI></ISTEX></double></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Merge
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 004397 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Merge/biblio.hfd -nk 004397 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Merge
|type= RBID
|clé= ISTEX:E5228823767CC6FDD6407DC4086EC5CC2B978A1C
|texte= Uniform stabilization for linear systems with persistency of excitation: the neutrally stable and the double integrator cases
}}
| This area was generated with Dilib version V0.6.33. |  |