On the real, rational, bounded, unit interpolation problem in ℋ ∞ and its applications to strong stabilization
One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in H ∞ satisfying certain interpolation conditions. The problem i...
Gespeichert in:
| Veröffentlicht in: | Transactions of the Institute of Measurement and Control 2019-01, Vol.41 (2), p.476-483 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 483 |
|---|---|
| container_issue | 2 |
| container_start_page | 476 |
| container_title | Transactions of the Institute of Measurement and Control |
| container_volume | 41 |
| creator | Yücesoy, Veysel Özbay, Hitay |
| description | One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in
H
∞
satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature. |
| doi_str_mv | 10.1177/0142331218759598 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2426122176</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sage_id>10.1177_0142331218759598</sage_id><sourcerecordid>2426122176</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2668-5a001d3274a85e7bd6e2034aa064b796cd16095744a28f0be1f58596d7419d3f3</originalsourceid><addsrcrecordid>eNp1UMtKxDAUDaLgOLp3GXA71STNo1nK4AsGZqPrkjbpmKGT1CRd6NqF4D_4cfMltjOCILg6l3se3HsAOMfoEmMhrhCmJM8xwYVgksniAEwwFSJDOZeHYDLS2cgfg5MY1wghSjmdgLB0MD0bGIxqZzCoZL0bp8r3Ths9g72zCVqXTOh8u6NhF3zVms2whdv3T7j9-ILKaWhThKrrWlvvZBEmD2MK3q0GUJVt7duOOAVHjWqjOfvBKXi6vXmc32eL5d3D_HqR1YTzImMKIaxzIqgqmBGV5oagnCqFOK2E5LXGHEkmKFWkaFBlcMMKJrkWFEudN_kUXOxzh3tfehNTufZ9GL6LJaGEY0Kw4IMK7VV18DEG05RdsBsVXkuMyrHZ8m-zgyXbW6Jamd_Qf_XfjXJ5gQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2426122176</pqid></control><display><type>article</type><title>On the real, rational, bounded, unit interpolation problem in ℋ ∞ and its applications to strong stabilization</title><source>SAGE Complete A-Z List</source><creator>Yücesoy, Veysel ; Özbay, Hitay</creator><creatorcontrib>Yücesoy, Veysel ; Özbay, Hitay</creatorcontrib><description>One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in
H
∞
satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature.</description><identifier>ISSN: 0142-3312</identifier><identifier>EISSN: 1477-0369</identifier><identifier>DOI: 10.1177/0142331218759598</identifier><language>eng</language><publisher>London, England: SAGE Publications</publisher><subject>Algorithms ; Feedback control ; H-infinity control ; Interpolation ; Stabilization</subject><ispartof>Transactions of the Institute of Measurement and Control, 2019-01, Vol.41 (2), p.476-483</ispartof><rights>The Author(s) 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2668-5a001d3274a85e7bd6e2034aa064b796cd16095744a28f0be1f58596d7419d3f3</citedby><cites>FETCH-LOGICAL-c2668-5a001d3274a85e7bd6e2034aa064b796cd16095744a28f0be1f58596d7419d3f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://journals.sagepub.com/doi/pdf/10.1177/0142331218759598$$EPDF$$P50$$Gsage$$H</linktopdf><linktohtml>$$Uhttps://journals.sagepub.com/doi/10.1177/0142331218759598$$EHTML$$P50$$Gsage$$H</linktohtml><link.rule.ids>314,780,784,21817,27922,27923,43619,43620</link.rule.ids></links><search><creatorcontrib>Yücesoy, Veysel</creatorcontrib><creatorcontrib>Özbay, Hitay</creatorcontrib><title>On the real, rational, bounded, unit interpolation problem in ℋ ∞ and its applications to strong stabilization</title><title>Transactions of the Institute of Measurement and Control</title><description>One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in
H
∞
satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature.</description><subject>Algorithms</subject><subject>Feedback control</subject><subject>H-infinity control</subject><subject>Interpolation</subject><subject>Stabilization</subject><issn>0142-3312</issn><issn>1477-0369</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1UMtKxDAUDaLgOLp3GXA71STNo1nK4AsGZqPrkjbpmKGT1CRd6NqF4D_4cfMltjOCILg6l3se3HsAOMfoEmMhrhCmJM8xwYVgksniAEwwFSJDOZeHYDLS2cgfg5MY1wghSjmdgLB0MD0bGIxqZzCoZL0bp8r3Ths9g72zCVqXTOh8u6NhF3zVms2whdv3T7j9-ILKaWhThKrrWlvvZBEmD2MK3q0GUJVt7duOOAVHjWqjOfvBKXi6vXmc32eL5d3D_HqR1YTzImMKIaxzIqgqmBGV5oagnCqFOK2E5LXGHEkmKFWkaFBlcMMKJrkWFEudN_kUXOxzh3tfehNTufZ9GL6LJaGEY0Kw4IMK7VV18DEG05RdsBsVXkuMyrHZ8m-zgyXbW6Jamd_Qf_XfjXJ5gQ</recordid><startdate>201901</startdate><enddate>201901</enddate><creator>Yücesoy, Veysel</creator><creator>Özbay, Hitay</creator><general>SAGE Publications</general><general>Sage Publications Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>L7M</scope></search><sort><creationdate>201901</creationdate><title>On the real, rational, bounded, unit interpolation problem in ℋ ∞ and its applications to strong stabilization</title><author>Yücesoy, Veysel ; Özbay, Hitay</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2668-5a001d3274a85e7bd6e2034aa064b796cd16095744a28f0be1f58596d7419d3f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>Feedback control</topic><topic>H-infinity control</topic><topic>Interpolation</topic><topic>Stabilization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yücesoy, Veysel</creatorcontrib><creatorcontrib>Özbay, Hitay</creatorcontrib><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Transactions of the Institute of Measurement and Control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yücesoy, Veysel</au><au>Özbay, Hitay</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the real, rational, bounded, unit interpolation problem in ℋ ∞ and its applications to strong stabilization</atitle><jtitle>Transactions of the Institute of Measurement and Control</jtitle><date>2019-01</date><risdate>2019</risdate><volume>41</volume><issue>2</issue><spage>476</spage><epage>483</epage><pages>476-483</pages><issn>0142-3312</issn><eissn>1477-0369</eissn><abstract>One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in
H
∞
satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature.</abstract><cop>London, England</cop><pub>SAGE Publications</pub><doi>10.1177/0142331218759598</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0142-3312 |
| ispartof | Transactions of the Institute of Measurement and Control, 2019-01, Vol.41 (2), p.476-483 |
| issn | 0142-3312 1477-0369 |
| language | eng |
| recordid | cdi_proquest_journals_2426122176 |
| source | SAGE Complete A-Z List |
| subjects | Algorithms Feedback control H-infinity control Interpolation Stabilization |
| title | On the real, rational, bounded, unit interpolation problem in ℋ ∞ and its applications to strong stabilization |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-09T11%3A26%3A34IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20real,%20rational,%20bounded,%20unit%20interpolation%20problem%20in%20%E2%84%8B%20%E2%88%9E%20and%20its%20applications%20to%20strong%20stabilization&rft.jtitle=Transactions%20of%20the%20Institute%20of%20Measurement%20and%20Control&rft.au=Y%C3%BCcesoy,%20Veysel&rft.date=2019-01&rft.volume=41&rft.issue=2&rft.spage=476&rft.epage=483&rft.pages=476-483&rft.issn=0142-3312&rft.eissn=1477-0369&rft_id=info:doi/10.1177/0142331218759598&rft_dat=%3Cproquest_cross%3E2426122176%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2426122176&rft_id=info:pmid/&rft_sage_id=10.1177_0142331218759598&rfr_iscdi=true |