ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME‐VARYING DELAYS
Identifieur interne : 002C81 ( Istex/Corpus ); précédent : 002C80; suivant : 002C82ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME‐VARYING DELAYS
Auteurs : S. M. Saadni ; M. Chaabane ; D. MehdiSource :
- Asian Journal of Control [ 1561-8625 ] ; 2006-03.
English descriptors
- Teeft :
- Admissible uncertainties, Appropriate dimension, Appropriate dimensions, Asian journal, Associate professor, Automatic control, Automatic control unit, Descriptor systems, Feedback, First derivatives, Generalized systems, Ieee trans, International conference, Lemma lemma, Matrix, Multiple delays, Neutral systems, Nominal system, Numerical example, Output feedback controller, Paper deals, Parameter uncertainties, Parameter uncertainty, Preparatory institute, Quadratic stability, Quadratic stabilization, Regular systems, Robust, Robust case, Robust control, Robust stability, Robust stability problem, Robust stabilization, Saadni, Schur complement, Singular delay system, Singular systems, Stability robustness, Stabilization, State delay, Sufficient conditions, System matrices, Theorem states, Theorem theorem, Uncertain case, Uncertain system, Uncertainty terms.
Abstract
This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time‐varying delays. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed‐loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method.
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DOI: 10.1111/j.1934-6093.2006.tb00245.x
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Saadni</name><affiliation><mods:affiliation>L.A.I.I., ESIP, Poitiers, France (e‐mail: driss.mehdi@univ‐poitiers.fr).</mods:affiliation></affiliation></author><author><name sortKey="Chaabane, M" sort="Chaabane, M" uniqKey="Chaabane M" first="M." last="Chaabane">M. Chaabane</name><affiliation><mods:affiliation>Automatic Control Unit, Preparatory Institute of Engineers, IPEIS, Sfax, Tunisia (e‐mail: mohamed.chaabane@ipeis.rnu.tn).</mods:affiliation></affiliation></author><author><name sortKey="Mehdi, D" sort="Mehdi, D" uniqKey="Mehdi D" first="D." last="Mehdi">D. 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M.</forename><surname>Saadni</surname></persName><affiliation><address><addrLine>L.A.I.I.</addrLine><addrLine>ESIP</addrLine><addrLine>Poitiers</addrLine><addrLine>France (e‐mail: driss.mehdi@univ‐poitiers.fr).</addrLine><country key="FR"></country></address></affiliation><email>driss.mehdi@univ‐poitiers.fr</email><note type="foot">Mohammed Salah Saadni was born in Annaba, Algeria, in 1977. He received the degree of engineer in automatic control from the University of Badji‐Mokhtar, Algeria, in 2000. He obtained the master degree in automatic control from the University of Poitiers, France. He is currently a Ph.D. student at Laboratoire d'Automatique et Informatique Industrielle (LAII) of the University of Poitiers. His research interests include robust control, time‐delay systems and LMI approach.</note></author><author xml:id="author-0001"><persName><forename type="first">M.</forename><surname>Chaabane</surname></persName><affiliation><orgName type="laboratory">Automatic Control Unit</orgName><orgName type="institution">Preparatory Institute of Engineers</orgName><address><addrLine>IPEIS</addrLine><addrLine>Sfax</addrLine><addrLine>Tunisia (e‐mail: mohamed.chaabane@ipeis.rnu.tn).</addrLine><country key="TN"></country></address></affiliation><email>mohamed.chaabane@ipeis.rnu.tn</email><note type="foot">Mohamed Chaabane was born in Sfax, Tunisia, on August 26, 1961. He received his doctorate degree in electrical engineering from the University of Nancy, France, in 1991. He was Associate Professor at the university of Nancy and is Researcher at Center of Automatic Control of Nancy (CRAN) from 1988–1992. He is currently Associate Professor in Automatic Control at Preparatory Institute of Engineers of Sfax, Tunisia. Since 1997, he is holding a research position at Automatic Control Unit, National School of Engineers of Sfax, Tunisia. His main research interests are robust control, optimal control, linear matrix inequalities, descriptor systems and applications of theses techniques to fed‐batch processes and agriculture systems. Dr. Chaabane is a member of the organization committees of several national and international conferences (international conference on Sciences and Techniques of Automatic control STA, international conference on Signals Systems Decision and information technology SSD).</note></author><author xml:id="author-0002"><persName><forename type="first">D.</forename><surname>Mehdi</surname></persName><affiliation><address><addrLine>L.A.I.I.</addrLine><addrLine>ESIP</addrLine><addrLine>Poitiers</addrLine><addrLine>France (e‐mail: driss.mehdi@univ‐poitiers.fr).</addrLine><country key="FR"></country></address></affiliation><email>driss.mehdi@univ‐poitiers.fr</email><note type="foot">Driss Mehdi was born in Oujda, Morocco in 1955. He recieved an engineer degree from Mohammadia Engineering School, Rabat, Morocco in 1979 and the Ph.D. in automatic control from Nancy University in 1986. He was Senior Lecturer from 1988 to 1992 in Louis Pasteur University in Strasbourg and from 1992 he was appointed as Professor in the University of Poitiers. His main interest are automatic control, nonlinear systems, robust control, LMIs, delay systems and singular systems.</note></author><idno type="istex">BCC7773F80E8C14C82DE1DB2206950A1F2C7CBAD</idno><idno type="ark">ark:/67375/WNG-VV15P9Q4-S</idno><idno type="DOI">10.1111/j.1934-6093.2006.tb00245.x</idno><idno type="unit">ASJC1</idno><idno type="toTypesetVersion">file:ASJC.ASJC1.pdf</idno></analytic><monogr><title level="j" type="main">Asian Journal of Control</title><title level="j" type="alt">ASIAN JOURNAL OF CONTROL</title><idno type="pISSN">1561-8625</idno><idno type="eISSN">1934-6093</idno><idno type="book-DOI">10.1002/(ISSN)1934-6093</idno><idno type="book-part-DOI">10.1111/asjc.2006.8.issue-1</idno><idno type="product">ASJC</idno><idno type="publisherDivision">ST</idno><imprint><biblScope unit="vol">8</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="11">11</biblScope><biblScope unit="page-count">11</biblScope><publisher>Blackwell Publishing Ltd</publisher><pubPlace>Oxford, UK</pubPlace><date type="published" when="2006-03"></date></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en" style="main"><head>ABSTRACT</head><p>This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time‐varying delays. 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Finally, a numerical example is provided to demonstrate the application of the proposed method.</p></abstract><textClass><keywords xml:lang="en"><term xml:id="k1">Singular systems</term><term xml:id="k2">multiple time‐varying delays</term><term xml:id="k3">robust stability</term><term xml:id="k4">robust stabilization</term><term xml:id="k5">linear matrix inequality</term></keywords><keywords rend="tocHeading1"><term>Original Article</term></keywords></textClass><langUsage><language ident="en"></language></langUsage></profileDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/ark:/67375/WNG-VV15P9Q4-S/fulltext.txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>Blackwell Publishing Ltd</publisherName><publisherLoc>Oxford, UK</publisherLoc></publisherInfo><doi origin="wiley" registered="yes">10.1002/(ISSN)1934-6093</doi><issn type="print">1561-8625</issn><issn type="electronic">1934-6093</issn><idGroup><id type="product" value="ASJC"></id><id type="publisherDivision" value="ST"></id></idGroup><titleGroup><title type="main" sort="ASIAN JOURNAL OF CONTROL">Asian Journal of Control</title></titleGroup></publicationMeta><publicationMeta level="part" position="03001"><doi origin="wiley">10.1111/asjc.2006.8.issue-1</doi><numberingGroup><numbering type="journalVolume" number="8">8</numbering><numbering type="journalIssue" number="1">1</numbering></numberingGroup><coverDate startDate="2006-03">March 2006</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="1" status="forIssue"><doi origin="wiley">10.1111/j.1934-6093.2006.tb00245.x</doi><idGroup><id type="unit" value="ASJC1"></id></idGroup><countGroup><count type="pageTotal" number="11"></count></countGroup><titleGroup><title type="tocHeading1">Original Article</title></titleGroup><copyright>© 2006 Asian Control Association/Chinese Automatic Control Society</copyright><eventGroup><event type="firstOnline" date="2008-10-22"></event><event type="publishedOnlineFinalForm" date="2008-10-22"></event><event type="xmlConverted" agent="Converter:BPG_TO_WML3G version:2.3.3 mode:FullText source:HeaderRef result:HeaderRef" date="2010-03-19"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-01-06"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.1.7 mode:FullText,remove_FC" date="2014-10-15"></event></eventGroup><numberingGroup><numbering type="pageFirst" number="1">1</numbering><numbering type="pageLast" number="11">11</numbering></numberingGroup><linkGroup><link type="toTypesetVersion" href="file:ASJC.ASJC1.pdf"></link></linkGroup></publicationMeta><contentMeta><unparsedEditorialHistory>Manuscript received April 28, 2005; accepted November 12, 2005.</unparsedEditorialHistory><countGroup><count type="referenceTotal" number="18"></count><count type="linksCrossRef" number="6"></count></countGroup><titleGroup><title type="main">ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME‐VARYING DELAYS</title></titleGroup><creators><creator creatorRole="author" xml:id="cr1" affiliationRef="#a1" noteRef="#fn1"><personName><givenNames>S. M.</givenNames><familyName>Saadni</familyName></personName></creator><creator creatorRole="author" xml:id="cr2" affiliationRef="#a2" noteRef="#fn2"><personName><givenNames>M.</givenNames><familyName>Chaabane</familyName></personName></creator><creator creatorRole="author" xml:id="cr3" affiliationRef="#a1" noteRef="#fn3"><personName><givenNames>D.</givenNames><familyName>Mehdi</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="a1" countryCode="FR"><unparsedAffiliation>L.A.I.I., ESIP, Poitiers, France (e‐mail: <email normalForm="driss.mehdi@univ-poitiers.fr">driss.mehdi@univ‐poitiers.fr</email>).</unparsedAffiliation></affiliation><affiliation xml:id="a2" countryCode="TN"><unparsedAffiliation>Automatic Control Unit, Preparatory Institute of Engineers, IPEIS, Sfax, Tunisia (e‐mail: <email>mohamed.chaabane@ipeis.rnu.tn</email>).</unparsedAffiliation></affiliation></affiliationGroup><keywordGroup xml:lang="en"><keyword xml:id="k1">Singular systems</keyword><keyword xml:id="k2">multiple time‐varying delays</keyword><keyword xml:id="k3">robust stability</keyword><keyword xml:id="k4">robust stabilization</keyword><keyword xml:id="k5">linear matrix inequality</keyword></keywordGroup><abstractGroup><abstract type="main" xml:lang="en"><title type="main">ABSTRACT</title><p>This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time‐varying delays. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed‐loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method.</p></abstract></abstractGroup></contentMeta><noteGroup><note xml:id="fn1"><label>3</label><p><b>Mohammed Salah Saadni</b> was born in Annaba, Algeria, in 1977. He received the degree of engineer in automatic control from the University of Badji‐Mokhtar, Algeria, in 2000. He obtained the master degree in automatic control from the University of Poitiers, France. He is currently a Ph.D. student at Laboratoire d'Automatique et Informatique Industrielle (LAII) of the University of Poitiers. His research interests include robust control, time‐delay systems and LMI approach.</p></note><note xml:id="fn2"><label>4</label><p><b>Mohamed Chaabane</b> was born in Sfax, Tunisia, on August 26, 1961. He received his doctorate degree in electrical engineering from the University of Nancy, France, in 1991. He was Associate Professor at the university of Nancy and is Researcher at Center of Automatic Control of Nancy (CRAN) from 1988–1992. He is currently Associate Professor in Automatic Control at Preparatory Institute of Engineers of Sfax, Tunisia. Since 1997, he is holding a research position at Automatic Control Unit, National School of Engineers of Sfax, Tunisia. His main research interests are robust control, optimal control, linear matrix inequalities, descriptor systems and applications of theses techniques to fed‐batch processes and agriculture systems. Dr. Chaabane is a member of the organization committees of several national and international conferences (international conference on Sciences and Techniques of Automatic control STA, international conference on Signals Systems Decision and information technology SSD).</p></note><note xml:id="fn3"><label>5</label><p><b>Driss Mehdi</b> was born in Oujda, Morocco in 1955. He recieved an engineer degree from Mohammadia Engineering School, Rabat, Morocco in 1979 and the Ph.D. in automatic control from Nancy University in 1986. He was Senior Lecturer from 1988 to 1992 in Louis Pasteur University in Strasbourg and from 1992 he was appointed as Professor in the University of Poitiers. His main interest are automatic control, nonlinear systems, robust control, LMIs, delay systems and singular systems.</p></note></noteGroup></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME‐VARYING DELAYS</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME‐VARYING DELAYS</title></titleInfo><name type="personal"><namePart type="given">S. M.</namePart><namePart type="family">Saadni</namePart><affiliation>L.A.I.I., ESIP, Poitiers, France (e‐mail: driss.mehdi@univ‐poitiers.fr).</affiliation><description>Mohammed Salah Saadni was born in Annaba, Algeria, in 1977. He received the degree of engineer in automatic control from the University of Badji‐Mokhtar, Algeria, in 2000. He obtained the master degree in automatic control from the University of Poitiers, France. He is currently a Ph.D. student at Laboratoire d'Automatique et Informatique Industrielle (LAII) of the University of Poitiers. His research interests include robust control, time‐delay systems and LMI approach.</description><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Chaabane</namePart><affiliation>Automatic Control Unit, Preparatory Institute of Engineers, IPEIS, Sfax, Tunisia (e‐mail: mohamed.chaabane@ipeis.rnu.tn).</affiliation><description>Mohamed Chaabane was born in Sfax, Tunisia, on August 26, 1961. He received his doctorate degree in electrical engineering from the University of Nancy, France, in 1991. He was Associate Professor at the university of Nancy and is Researcher at Center of Automatic Control of Nancy (CRAN) from 1988–1992. He is currently Associate Professor in Automatic Control at Preparatory Institute of Engineers of Sfax, Tunisia. Since 1997, he is holding a research position at Automatic Control Unit, National School of Engineers of Sfax, Tunisia. His main research interests are robust control, optimal control, linear matrix inequalities, descriptor systems and applications of theses techniques to fed‐batch processes and agriculture systems. Dr. Chaabane is a member of the organization committees of several national and international conferences (international conference on Sciences and Techniques of Automatic control STA, international conference on Signals Systems Decision and information technology SSD).</description><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Mehdi</namePart><affiliation>L.A.I.I., ESIP, Poitiers, France (e‐mail: driss.mehdi@univ‐poitiers.fr).</affiliation><description>Driss Mehdi was born in Oujda, Morocco in 1955. He recieved an engineer degree from Mohammadia Engineering School, Rabat, Morocco in 1979 and the Ph.D. in automatic control from Nancy University in 1986. He was Senior Lecturer from 1988 to 1992 in Louis Pasteur University in Strasbourg and from 1992 he was appointed as Professor in the University of Poitiers. His main interest are automatic control, nonlinear systems, robust control, LMIs, delay systems and singular systems.</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre><originInfo><publisher>Blackwell Publishing Ltd</publisher><place><placeTerm type="text">Oxford, UK</placeTerm></place><dateIssued encoding="w3cdtf">2006-03</dateIssued><edition>Manuscript received April 28, 2005; accepted November 12, 2005.</edition><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><extent unit="references">18</extent><extent unit="linksCrossRef">6</extent></physicalDescription><abstract lang="en">This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time‐varying delays. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed‐loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method.</abstract><subject lang="en"><genre>keywords</genre><topic>Singular systems</topic><topic>multiple time‐varying delays</topic><topic>robust stability</topic><topic>robust stabilization</topic><topic>linear matrix inequality</topic></subject><relatedItem type="host"><titleInfo><title>Asian Journal of Control</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><identifier type="ISSN">1561-8625</identifier><identifier type="eISSN">1934-6093</identifier><identifier type="DOI">10.1002/(ISSN)1934-6093</identifier><identifier type="PublisherID">ASJC</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>8</number></detail><detail type="issue"><caption>no.</caption><number>1</number></detail><extent unit="pages"><start>1</start><end>11</end><total>11</total></extent></part></relatedItem><identifier type="istex">BCC7773F80E8C14C82DE1DB2206950A1F2C7CBAD</identifier><identifier type="ark">ark:/67375/WNG-VV15P9Q4-S</identifier><identifier type="DOI">10.1111/j.1934-6093.2006.tb00245.x</identifier><identifier type="ArticleID">ASJC1</identifier><accessCondition type="use and reproduction" contentType="copyright">© 2006 Asian Control Association/Chinese Automatic Control Society</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-L0C46X92-X">wiley</recordContentSource><recordOrigin>Blackwell Publishing Ltd</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/WNG-VV15P9Q4-S/record.json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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