Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases
Identifieur interne : 003524 ( Hal/Checkpoint ); précédent : 003523; suivant : 003525Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases
Auteurs : Antoine Chaillet [Italie] ; Yacine Chitour [France] ; Antonio Loría [France] ; Mario Sigalotti [France]Source :
- Mathematics of Control, Signals, and Systems [ 0932-4194 ] ; 2008.
English descriptors
Abstract
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.
Url:
DOI: 10.1007/s00498-008-0024-1
Links toward previous steps (curation, corpus...)
Links to Exploration step
Hal:hal-00132968Le document en format XML
<record><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></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 api="V3"><titleStmt><title xml:lang="en">Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases</title><author role="aut"><persName><forename type="first">Antoine</forename><surname>Chaillet</surname></persName><email></email><idno type="idhal">antoinechaillet</idno><idno type="halauthor">166309</idno><affiliation ref="#struct-30081"></affiliation></author><author role="aut"><persName><forename type="first">Yacine</forename><surname>Chitour</surname></persName><email></email><idno type="halauthor">98392</idno><affiliation ref="#struct-1289"></affiliation></author><author role="aut"><persName><forename type="first">Antonio</forename><surname>Loría</surname></persName><email></email><idno type="halauthor">166310</idno><affiliation ref="#struct-1289"></affiliation></author><author role="aut"><persName><forename type="first">Mario</forename><surname>Sigalotti</surname></persName><email>Mario.Sigalotti@loria.fr</email><idno type="halauthor">120773</idno><affiliation ref="#struct-2368"></affiliation><affiliation ref="#struct-23"></affiliation><affiliation ref="#struct-2496"></affiliation></author><editor role="depositor"><persName><forename>Mario</forename><surname>Sigalotti</surname></persName><email>Mario.Sigalotti@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2007-02-23 10:55:58</date><date type="whenModified">2016-03-21 17:50:01</date><date type="whenReleased">2007-02-23 11:28:46</date><date type="whenProduced">2008</date><date type="whenEndEmbargoed">2007-02-23</date><ref type="file" target="https://hal.archives-ouvertes.fr/hal-00132968/document"><date notBefore="2007-02-23"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.archives-ouvertes.fr/hal-00132968/file/CCLS.pdf"><date notBefore="2007-02-23"></date></ref></edition><respStmt><resp>contributor</resp><name key="112750"><persName><forename>Mario</forename><surname>Sigalotti</surname></persName><email>Mario.Sigalotti@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-00132968</idno><idno type="halUri">https://hal.archives-ouvertes.fr/hal-00132968</idno><idno type="halBibtex">chaillet:hal-00132968</idno><idno type="halRefHtml">Mathematics of Control, Signals, and Systems, Springer Verlag, 2008, 20 (2), pp.135-156. <10.1007/s00498-008-0024-1></idno><idno type="halRef">Mathematics of Control, Signals, and Systems, Springer Verlag, 2008, 20 (2), pp.135-156. <10.1007/s00498-008-0024-1></idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="IECN">IECN - Institut Elie Cartan Nancy</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="UNIV-METZ">Université Paul Verlaine - Metz</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno><idno type="stamp" n="L2S">Laboratoire des signaux et systèmes</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="SUP_SYSTEMES" p="CENTRALESUPELEC">Pôle Systèmes</idno><idno type="stamp" n="SUP_LSS" p="CENTRALESUPELEC">Laboratoire des Signaux et Systèmes</idno><idno type="stamp" n="SUPELEC">SUPELEC</idno><idno type="stamp" n="INRIA2">INRIA 2</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="CENTRALESUPELEC">Ecole CentraleSupélec</idno><idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno></seriesStmt><notesStmt><note type="audience" n="2">International</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note></notesStmt><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 role="aut"><persName><forename type="first">Antoine</forename><surname>Chaillet</surname></persName><idno type="idHal">antoinechaillet</idno><idno type="halAuthorId">166309</idno><affiliation ref="#struct-30081"></affiliation></author><author role="aut"><persName><forename type="first">Yacine</forename><surname>Chitour</surname></persName><idno type="halAuthorId">98392</idno><affiliation ref="#struct-1289"></affiliation></author><author role="aut"><persName><forename type="first">Antonio</forename><surname>Loría</surname></persName><idno type="halAuthorId">166310</idno><affiliation ref="#struct-1289"></affiliation></author><author role="aut"><persName><forename type="first">Mario</forename><surname>Sigalotti</surname></persName><email>Mario.Sigalotti@loria.fr</email><idno type="halAuthorId">120773</idno><affiliation ref="#struct-2368"></affiliation><affiliation ref="#struct-23"></affiliation><affiliation ref="#struct-2496"></affiliation></author></analytic><monogr><idno type="halJournalId" status="VALID">16937</idno><idno type="issn">0932-4194</idno><idno type="eissn">1435-568X</idno><title level="j">Mathematics of Control, Signals, and Systems</title><imprint><publisher>Springer Verlag</publisher><biblScope unit="volume">20</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="pp">135-156</biblScope><date type="datePub">2008</date></imprint></monogr><idno type="arxiv">math.OC/0702687</idno><idno type="doi">10.1007/s00498-008-0024-1</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">uniform stability</term><term xml:lang="en">switching system</term><term xml:lang="en">permanent excitation</term></keywords><classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode><classCode scheme="halDomain" n="spi.auto">Engineering Sciences [physics]/Automatic</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><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.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Hal/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 003524 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Hal/Checkpoint/biblio.hfd -nk 003524 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Hal
|étape= Checkpoint
|type= RBID
|clé= Hal:hal-00132968
|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. |  |