Robust stability and stabilization for singular systems with state delay and parameter uncertainty
Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. 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, imp...
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| Veröffentlicht in: | IEEE transactions on automatic control 2002-07, Vol.47 (7), p.1122-1128 |
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| container_end_page | 1128 |
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| container_issue | 7 |
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| container_title | IEEE transactions on automatic control |
| container_volume | 47 |
| creator | Shengyuan Xu Van Dooren, P. Stefan, R. Lam, J. |
| description | Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. 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, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method. |
| doi_str_mv | 10.1109/TAC.2002.800651 |
| format | Article |
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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, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. 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(IEEE) 2002</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c482t-c162e9a0c813beff17cba7eaa6cf7e81375b8c6906b2f8e1b8cf1655b910c5b33</citedby><cites>FETCH-LOGICAL-c482t-c162e9a0c813beff17cba7eaa6cf7e81375b8c6906b2f8e1b8cf1655b910c5b33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1017556$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>315,782,786,798,27933,27934,54767</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1017556$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14291890$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Shengyuan Xu</creatorcontrib><creatorcontrib>Van Dooren, P.</creatorcontrib><creatorcontrib>Stefan, R.</creatorcontrib><creatorcontrib>Lam, J.</creatorcontrib><title>Robust stability and stabilization for singular systems with state delay and parameter uncertainty</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. 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, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.</description><subject>Applied sciences</subject><subject>Automatic control</subject><subject>Computer science; control theory; systems</subject><subject>Control system analysis</subject><subject>Control systems</subject><subject>Control theory. Systems</subject><subject>Delay</subject><subject>Delay systems</subject><subject>Design engineering</subject><subject>Exact sciences and technology</subject><subject>Law</subject><subject>Linear matrix inequalities</subject><subject>Mathematical models</subject><subject>Optimal control</subject><subject>Riccati equations</subject><subject>Robust control</subject><subject>Robust stability</subject><subject>Stability</subject><subject>Stabilization</subject><subject>State feedback</subject><subject>Stochastic processes</subject><subject>Uncertain systems</subject><subject>Uncertainty</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqN0U1rFTEUBuAgCl6raxduBkFdzW0-Jl_LclErFAqlXYeT9IymzJ25Jhnk-uvNMBWlC-0qOeE57yIvIa8Z3TJG7en12W7LKeVbQ6mS7AnZMClNyyUXT8mGUmZay416Tl7kfFdH1XVsQ_zV5OdcmlzAxyGWYwPj7e_pJ5Q4jU0_pSbH8es8QL0cc8F9bn7E8m1xBZtbHGDdO0CCPRZMzTwGTAXiWI4vybMehoyv7s8TcvPp4_XuvL24_Pxld3bRhs7w0gamOFqgwTDhse-ZDh40AqjQa6yPWnoTlKXK894gq0PPlJTeMhqkF-KEfFhzD2n6PmMubh9zwGGAEac5O0u1lYbqRb7_p-SWMquF-T80shPCPAJqZaTSXYVvH8C7aU5j_RdnTCekVWZBpysKaco5Ye8OKe4hHR2jbinb1bLdUrZby64b7-5jIQcY-gRjiPnPWsctM5ZW92Z1ERH_SmVaSiV-AULDszY</recordid><startdate>20020701</startdate><enddate>20020701</enddate><creator>Shengyuan Xu</creator><creator>Van Dooren, P.</creator><creator>Stefan, R.</creator><creator>Lam, J.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Systems</topic><topic>Delay</topic><topic>Delay systems</topic><topic>Design engineering</topic><topic>Exact sciences and technology</topic><topic>Law</topic><topic>Linear matrix inequalities</topic><topic>Mathematical models</topic><topic>Optimal control</topic><topic>Riccati equations</topic><topic>Robust control</topic><topic>Robust stability</topic><topic>Stability</topic><topic>Stabilization</topic><topic>State feedback</topic><topic>Stochastic processes</topic><topic>Uncertain systems</topic><topic>Uncertainty</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shengyuan Xu</creatorcontrib><creatorcontrib>Van Dooren, P.</creatorcontrib><creatorcontrib>Stefan, R.</creatorcontrib><creatorcontrib>Lam, J.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Aerospace Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Shengyuan Xu</au><au>Van Dooren, P.</au><au>Stefan, R.</au><au>Lam, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robust stability and stabilization for singular systems with state delay and parameter uncertainty</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2002-07-01</date><risdate>2002</risdate><volume>47</volume><issue>7</issue><spage>1122</spage><epage>1128</epage><pages>1122-1128</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. 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, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. 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| identifier | ISSN: 0018-9286 |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Automatic control Computer science control theory systems Control system analysis Control systems Control theory. Systems Delay Delay systems Design engineering Exact sciences and technology Law Linear matrix inequalities Mathematical models Optimal control Riccati equations Robust control Robust stability Stability Stabilization State feedback Stochastic processes Uncertain systems Uncertainty |
| title | Robust stability and stabilization for singular systems with state delay and parameter uncertainty |
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