Synthesis of minimal linear stabilizers
We consider the stabilizer synthesis problem for linear stationary control dynamical systems; attention is mainly focused on the investigation of possibilities to reduce the order of such stabilizers. The problem is considered in two settings. The first setting deals with the construction of stabili...
Gespeichert in:
| Veröffentlicht in: | Differential equations 2009-05, Vol.45 (5), p.694-703 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 703 |
|---|---|
| container_issue | 5 |
| container_start_page | 694 |
| container_title | Differential equations |
| container_volume | 45 |
| creator | Il’in, A. V. Korovin, S. K. Fomichev, V. V. |
| description | We consider the stabilizer synthesis problem for linear stationary control dynamical systems; attention is mainly focused on the investigation of possibilities to reduce the order of such stabilizers. The problem is considered in two settings. The first setting deals with the construction of stabilizers of given order (in particular, the minimum possible order); no conditions are imposed on the spectrum of the closed system. For scalar (single-input-single-output) control systems, we suggest an approach to the solution of this problem and obtain necessary and sufficient conditions for the existence of a stabilizer of a given order. The second problem is that of synthesizing a stabilizer of minimum order with given dynamic properties (a given spectrum or a given distribution of the spectrum of the closed system, in particular, with a guaranteed convergence rate of the closed system). For this problem, we suggest two approaches that permit one to obtain an upper bound for the dimension of such stabilizers. |
| doi_str_mv | 10.1134/S0012266109050085 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_36431806</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1894335701</sourcerecordid><originalsourceid>FETCH-LOGICAL-c346t-ca876dfdd0ba3ccd25b42fcb2af23ea57205ac79d815357a91ada77bb322b1bf3</originalsourceid><addsrcrecordid>eNp1kE9LAzEUxIMoWKsfwNviQU-r7yWbZPcoxX9Q8FA9hySbaMp2tybbQ_30plQQFE_vML8Z5g0h5wjXiKy6WQAgpUIgNMABan5AJiigLhnU7JBMdnK504_JSUpLAGgk8gm5Wmz78d2lkIrBF6vQh5Xuii70TscijdqELny6mE7Jkdddcmffd0pe7-9eZo_l_PnhaXY7Ly2rxFhaXUvR-rYFo5m1LeWmot4aqj1lTnNJgWsrm7ZGzrjUDepWS2kMo9Sg8WxKLve56zh8bFwa1Sok67pO927YJMVExbAGkcGLX-By2MQ-d1OUcYQ6z5Ih3EM2DilF59U65gfjViGo3W7qz27ZQ_eelNn-zcWf4P9NX33FbiI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>235108113</pqid></control><display><type>article</type><title>Synthesis of minimal linear stabilizers</title><source>SpringerLink Journals - AutoHoldings</source><creator>Il’in, A. V. ; Korovin, S. K. ; Fomichev, V. V.</creator><creatorcontrib>Il’in, A. V. ; Korovin, S. K. ; Fomichev, V. V.</creatorcontrib><description>We consider the stabilizer synthesis problem for linear stationary control dynamical systems; attention is mainly focused on the investigation of possibilities to reduce the order of such stabilizers. The problem is considered in two settings. The first setting deals with the construction of stabilizers of given order (in particular, the minimum possible order); no conditions are imposed on the spectrum of the closed system. For scalar (single-input-single-output) control systems, we suggest an approach to the solution of this problem and obtain necessary and sufficient conditions for the existence of a stabilizer of a given order. The second problem is that of synthesizing a stabilizer of minimum order with given dynamic properties (a given spectrum or a given distribution of the spectrum of the closed system, in particular, with a guaranteed convergence rate of the closed system). For this problem, we suggest two approaches that permit one to obtain an upper bound for the dimension of such stabilizers.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266109050085</identifier><language>eng</language><publisher>Dordrecht: SP MAIK Nauka/Interperiodica</publisher><subject>Control Theory ; Difference and Functional Equations ; Differential equations ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations ; Polynomials ; Studies</subject><ispartof>Differential equations, 2009-05, Vol.45 (5), p.694-703</ispartof><rights>Pleiades Publishing, Ltd. 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c346t-ca876dfdd0ba3ccd25b42fcb2af23ea57205ac79d815357a91ada77bb322b1bf3</citedby><cites>FETCH-LOGICAL-c346t-ca876dfdd0ba3ccd25b42fcb2af23ea57205ac79d815357a91ada77bb322b1bf3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266109050085$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266109050085$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Il’in, A. V.</creatorcontrib><creatorcontrib>Korovin, S. K.</creatorcontrib><creatorcontrib>Fomichev, V. V.</creatorcontrib><title>Synthesis of minimal linear stabilizers</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>We consider the stabilizer synthesis problem for linear stationary control dynamical systems; attention is mainly focused on the investigation of possibilities to reduce the order of such stabilizers. The problem is considered in two settings. The first setting deals with the construction of stabilizers of given order (in particular, the minimum possible order); no conditions are imposed on the spectrum of the closed system. For scalar (single-input-single-output) control systems, we suggest an approach to the solution of this problem and obtain necessary and sufficient conditions for the existence of a stabilizer of a given order. The second problem is that of synthesizing a stabilizer of minimum order with given dynamic properties (a given spectrum or a given distribution of the spectrum of the closed system, in particular, with a guaranteed convergence rate of the closed system). For this problem, we suggest two approaches that permit one to obtain an upper bound for the dimension of such stabilizers.</description><subject>Control Theory</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Polynomials</subject><subject>Studies</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kE9LAzEUxIMoWKsfwNviQU-r7yWbZPcoxX9Q8FA9hySbaMp2tybbQ_30plQQFE_vML8Z5g0h5wjXiKy6WQAgpUIgNMABan5AJiigLhnU7JBMdnK504_JSUpLAGgk8gm5Wmz78d2lkIrBF6vQh5Xuii70TscijdqELny6mE7Jkdddcmffd0pe7-9eZo_l_PnhaXY7Ly2rxFhaXUvR-rYFo5m1LeWmot4aqj1lTnNJgWsrm7ZGzrjUDepWS2kMo9Sg8WxKLve56zh8bFwa1Sok67pO927YJMVExbAGkcGLX-By2MQ-d1OUcYQ6z5Ih3EM2DilF59U65gfjViGo3W7qz27ZQ_eelNn-zcWf4P9NX33FbiI</recordid><startdate>20090501</startdate><enddate>20090501</enddate><creator>Il’in, A. V.</creator><creator>Korovin, S. K.</creator><creator>Fomichev, V. V.</creator><general>SP MAIK Nauka/Interperiodica</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>04Q</scope><scope>04W</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>20090501</creationdate><title>Synthesis of minimal linear stabilizers</title><author>Il’in, A. V. ; Korovin, S. K. ; Fomichev, V. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c346t-ca876dfdd0ba3ccd25b42fcb2af23ea57205ac79d815357a91ada77bb322b1bf3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Control Theory</topic><topic>Difference and Functional Equations</topic><topic>Differential equations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>Polynomials</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Il’in, A. V.</creatorcontrib><creatorcontrib>Korovin, S. K.</creatorcontrib><creatorcontrib>Fomichev, V. V.</creatorcontrib><collection>CrossRef</collection><collection>India Database</collection><collection>India Database: Science & Technology</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering 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>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Il’in, A. V.</au><au>Korovin, S. K.</au><au>Fomichev, V. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Synthesis of minimal linear stabilizers</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2009-05-01</date><risdate>2009</risdate><volume>45</volume><issue>5</issue><spage>694</spage><epage>703</epage><pages>694-703</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>We consider the stabilizer synthesis problem for linear stationary control dynamical systems; attention is mainly focused on the investigation of possibilities to reduce the order of such stabilizers. The problem is considered in two settings. The first setting deals with the construction of stabilizers of given order (in particular, the minimum possible order); no conditions are imposed on the spectrum of the closed system. For scalar (single-input-single-output) control systems, we suggest an approach to the solution of this problem and obtain necessary and sufficient conditions for the existence of a stabilizer of a given order. The second problem is that of synthesizing a stabilizer of minimum order with given dynamic properties (a given spectrum or a given distribution of the spectrum of the closed system, in particular, with a guaranteed convergence rate of the closed system). For this problem, we suggest two approaches that permit one to obtain an upper bound for the dimension of such stabilizers.</abstract><cop>Dordrecht</cop><pub>SP MAIK Nauka/Interperiodica</pub><doi>10.1134/S0012266109050085</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0012-2661 |
| ispartof | Differential equations, 2009-05, Vol.45 (5), p.694-703 |
| issn | 0012-2661 1608-3083 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_36431806 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Control Theory Difference and Functional Equations Differential equations Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Polynomials Studies |
| title | Synthesis of minimal linear stabilizers |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T22%3A26%3A12IST&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=Synthesis%20of%20minimal%20linear%20stabilizers&rft.jtitle=Differential%20equations&rft.au=Il%E2%80%99in,%20A.%20V.&rft.date=2009-05-01&rft.volume=45&rft.issue=5&rft.spage=694&rft.epage=703&rft.pages=694-703&rft.issn=0012-2661&rft.eissn=1608-3083&rft_id=info:doi/10.1134/S0012266109050085&rft_dat=%3Cproquest_cross%3E1894335701%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=235108113&rft_id=info:pmid/&rfr_iscdi=true |