<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-01141266</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-04-29T06:42:11+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A descriptor Takagi-Sugeno approach to frequency weighted nonlinear model reduction</title>
            <author role="aut">
              <persName>
                <forename type="first">Benoît</forename>
                <surname>Marx</surname>
              </persName>
              <email type="md5">63e61dfc5d46a20e7b2c962bd7fa429f</email>
              <email type="domain">univ-lorraine.fr</email>
              <idno type="idhal" notation="string">benoitmarx</idno>
              <idno type="idhal" notation="numeric">13558</idno>
              <idno type="halauthorid" notation="string">15226-13558</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/M-4145-2015</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2553-256X</idno>
              <idno type="IDREF">https://www.idref.fr/07774795X</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/M-4145-2015</idno>
              <affiliation ref="#struct-185180"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Benoit</forename>
                <surname>Marx</surname>
              </persName>
              <email type="md5">63e61dfc5d46a20e7b2c962bd7fa429f</email>
              <email type="domain">univ-lorraine.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2021-11-25 09:34:23</date>
              <date type="whenWritten">2015</date>
              <date type="whenModified">2025-11-04 12:00:12</date>
              <date type="whenReleased">2021-11-26 16:52:58</date>
              <date type="whenProduced">2015-08-02</date>
              <date type="whenEndEmbargoed">2021-11-25</date>
              <ref type="file" target="https://hal.science/hal-01141266v1/document">
                <date notBefore="2021-11-25"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01141266v1/file/2015_FUZZ_MARX.pdf" id="file-3448244-3026860">
                <date notBefore="2021-11-25"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="105682">
                <persName>
                  <forename>Benoit</forename>
                  <surname>Marx</surname>
                </persName>
                <email type="md5">63e61dfc5d46a20e7b2c962bd7fa429f</email>
                <email type="domain">univ-lorraine.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01141266</idno>
            <idno type="halUri">https://hal.science/hal-01141266</idno>
            <idno type="halBibtex">marx:hal-01141266</idno>
            <idno type="halRefHtml">&lt;i&gt;IEEE International Conference on Fuzzy Systems, FuzzIEEE 2015&lt;/i&gt;, Aug 2015, Istanbul, Turkey. pp.1-7, &lt;a target="_blank" href="https://dx.doi.org/10.1109/FUZZ-IEEE.2015.7337985"&gt;&amp;#x27E8;10.1109/FUZZ-IEEE.2015.7337985&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">IEEE International Conference on Fuzzy Systems, FuzzIEEE 2015, Aug 2015, Istanbul, Turkey. pp.1-7, &amp;#x27E8;10.1109/FUZZ-IEEE.2015.7337985&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3448244-3026860"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="CRAN-CID" corresp="CRAN">CRAN-CID</idno>
            <idno type="stamp" n="CRAN">Centre de Recherche en Automatique de Nancy</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="AM2I-UL">Pôle scientifique Automatique, Mathématiques, Informatique et leurs Intéractions de l'Université de Lorraine</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A descriptor Takagi-Sugeno approach to frequency weighted nonlinear model reduction</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Benoît</forename>
                    <surname>Marx</surname>
                  </persName>
                  <email type="md5">63e61dfc5d46a20e7b2c962bd7fa429f</email>
                  <email type="domain">univ-lorraine.fr</email>
                  <idno type="idhal" notation="string">benoitmarx</idno>
                  <idno type="idhal" notation="numeric">13558</idno>
                  <idno type="halauthorid" notation="string">15226-13558</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/M-4145-2015</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2553-256X</idno>
                  <idno type="IDREF">https://www.idref.fr/07774795X</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/M-4145-2015</idno>
                  <affiliation ref="#struct-185180"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">CID</idno>
                <title level="m">IEEE International Conference on Fuzzy Systems</title>
                <meeting>
                  <title>IEEE International Conference on Fuzzy Systems, FuzzIEEE 2015</title>
                  <date type="start">2015-08-02</date>
                  <date type="end">2015-08-05</date>
                  <settlement>Istanbul</settlement>
                  <country key="TR">Turkey</country>
                </meeting>
                <imprint>
                  <biblScope unit="pp">1-7</biblScope>
                  <date type="datePub">2015</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1109/FUZZ-IEEE.2015.7337985</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">L2 approach</term>
                <term xml:lang="en">Takagi–Sugeno systems</term>
                <term xml:lang="en">Model reduction</term>
                <term xml:lang="en">Descriptor systems</term>
                <term xml:lang="en">Linear Matrix Inequality</term>
              </keywords>
              <classCode scheme="halDomain" n="spi.auto">Engineering Sciences [physics]/Automatic</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this note, the problem of frequency weighted nonlinear model reduction is addressed. It consists in approximating a given nonlinear system of order n by a nonlinear system of order k, where k &lt; n. The goal is to compute the reduced order system minimizing the L_2-gain from the input to the difference between the outputs of the original and the reduced systems. For this purpose the nonlinear system generating the approximation error is written under the descriptor Takagi-Sugeno formalism and is studied with the use of a multiple Lyapunov function, based on the descriptor approach. The obtained results are expressed in terms of Linear Matrix Inequalities (LMI) and the matrices defining the reduced order system are obtained as a result of LMI problem.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-185180" status="VALID">
          <idno type="IdRef">03500472X</idno>
          <idno type="ISNI">0000000121518763</idno>
          <idno type="RNSR">200112440X</idno>
          <idno type="IdUnivLorraine">[UL]RSA--</idno>
          <idno type="ROR">https://ror.org/022r5hc56</idno>
          <orgName>Centre de Recherche en Automatique de Nancy</orgName>
          <orgName type="acronym">CRAN</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Université de Lorraine, Campus Sciences, BP 70239, 54506 Vandoeuvre-les-Nancy Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cran.univ-lorraine.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413289" type="direct"/>
            <relation name="UMR7039" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-413289" status="VALID">
          <idno type="IdRef">157040569</idno>
          <idno type="IdUnivLorraine">[UL]100--</idno>
          <idno type="ROR">https://ror.org/04vfs2w97</idno>
          <orgName>Université de Lorraine</orgName>
          <orgName type="acronym">UL</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lorraine.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</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"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>