Combination of Lyapunov and Density Functions for Stability of Rotational Motion
Lyapunov methods and density functions provide dual characterizations of the solutions of a nonlinear dynamic system. This work exploits the idea of combining both techniques, to yield stability results that are valid for almost all the solutions of the system. Based on the combination of Lyapunov a...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on automatic control 2011-11, Vol.56 (11), p.2599-2607 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2607 |
|---|---|
| container_issue | 11 |
| container_start_page | 2599 |
| container_title | IEEE transactions on automatic control |
| container_volume | 56 |
| creator | Fernandes Vasconcelos, José Rantzer, Anders Silvestre, C. Oliveira, P. J. |
| description | Lyapunov methods and density functions provide dual characterizations of the solutions of a nonlinear dynamic system. This work exploits the idea of combining both techniques, to yield stability results that are valid for almost all the solutions of the system. Based on the combination of Lyapunov and density functions, analysis methods are proposed for the derivation of almost input-to-state stability, and of almost global stability in nonlinear systems. The techniques are illustrated for an inertial attitude observer, where angular velocity readings are corrupted by non-idealities. |
| doi_str_mv | 10.1109/TAC.2011.2123290 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_proquest_journals_901632932</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>5725165</ieee_id><sourcerecordid>963921194</sourcerecordid><originalsourceid>FETCH-LOGICAL-c487t-9769e9b81dfacbaf6bce27b4fc9df08b11717a87c254d1285ab5c59b5f4700343</originalsourceid><addsrcrecordid>eNpdkUuLFDEUhYMo2M64F9wUgriqnty8sxxaR4UWh3FchySVQIbqSlmpUvrfm7KbXri45PWdc8M9CL0BvAXA-ubxdrclGGBLgFCi8TO0Ac5VSzihz9EGY1CtJkq8RK9KeapHwRhs0P0uH1wa7Jzy0OTY7I92XIb8u7FD13wMQ0nzsblbBr8CpYl5an7M1qV-va_8Q57_aW3ffMvr5hq9iLYv4fV5vUI_7z497r60---fv-5u961nSs6tlkIH7RR00Xpno3A-EOlY9LqLWDkACdIq6QlnHRDFreOea8cjkxhTRq_Q_uRb_oRxcWac0sFOR5NtMv0y1nK1TAlGEsqY6jqjNHDDSMeMtUIaDLx2igqikNXuw8lunPKvJZTZHFLxoe_tEPJSjBZUEwC9Nn73H_mUl6kOoEJ1qnX2lFQInyA_5VKmEC__A2zWvEzNy6x5mXNeVfL-7GuLt32c7OBTueiIYJhRJSr39sSlEMLlmUvCQXD6F31VnLE</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>901632932</pqid></control><display><type>article</type><title>Combination of Lyapunov and Density Functions for Stability of Rotational Motion</title><source>IEEE Electronic Library (IEL)</source><creator>Fernandes Vasconcelos, José ; Rantzer, Anders ; Silvestre, C. ; Oliveira, P. J.</creator><creatorcontrib>Fernandes Vasconcelos, José ; Rantzer, Anders ; Silvestre, C. ; Oliveira, P. J.</creatorcontrib><description>Lyapunov methods and density functions provide dual characterizations of the solutions of a nonlinear dynamic system. This work exploits the idea of combining both techniques, to yield stability results that are valid for almost all the solutions of the system. Based on the combination of Lyapunov and density functions, analysis methods are proposed for the derivation of almost input-to-state stability, and of almost global stability in nonlinear systems. The techniques are illustrated for an inertial attitude observer, where angular velocity readings are corrupted by non-idealities.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2011.2123290</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Angular velocity ; Applied sciences ; Asymptotic stability ; Computer science; control theory; systems ; Control Engineering ; Control system analysis ; Control theory. Systems ; Density ; Density functional theory ; density functions ; Derivation ; Dynamical systems ; Electrical Engineering, Electronic Engineering, Information Engineering ; Elektroteknik och elektronik ; Engineering and Technology ; Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; input-to-state stability ; Lyapunov method ; Lyapunov methods ; Modelling and identification ; Noise ; Nonlinear dynamics ; Observers ; Physics ; Reglerteknik ; Rotational ; Solid dynamics (ballistics, collision, multibody system, stabilization...) ; Solid mechanics ; Stability ; Stability criteria ; Teknik ; Trajectory</subject><ispartof>IEEE transactions on automatic control, 2011-11, Vol.56 (11), p.2599-2607</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Nov 2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c487t-9769e9b81dfacbaf6bce27b4fc9df08b11717a87c254d1285ab5c59b5f4700343</citedby><cites>FETCH-LOGICAL-c487t-9769e9b81dfacbaf6bce27b4fc9df08b11717a87c254d1285ab5c59b5f4700343</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/5725165$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,315,554,782,786,798,887,27933,27934,54767</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/5725165$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26404386$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://lup.lub.lu.se/record/2203240$$DView record from Swedish Publication Index$$Hfree_for_read</backlink></links><search><creatorcontrib>Fernandes Vasconcelos, José</creatorcontrib><creatorcontrib>Rantzer, Anders</creatorcontrib><creatorcontrib>Silvestre, C.</creatorcontrib><creatorcontrib>Oliveira, P. J.</creatorcontrib><title>Combination of Lyapunov and Density Functions for Stability of Rotational Motion</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>Lyapunov methods and density functions provide dual characterizations of the solutions of a nonlinear dynamic system. This work exploits the idea of combining both techniques, to yield stability results that are valid for almost all the solutions of the system. Based on the combination of Lyapunov and density functions, analysis methods are proposed for the derivation of almost input-to-state stability, and of almost global stability in nonlinear systems. The techniques are illustrated for an inertial attitude observer, where angular velocity readings are corrupted by non-idealities.</description><subject>Angular velocity</subject><subject>Applied sciences</subject><subject>Asymptotic stability</subject><subject>Computer science; control theory; systems</subject><subject>Control Engineering</subject><subject>Control system analysis</subject><subject>Control theory. Systems</subject><subject>Density</subject><subject>Density functional theory</subject><subject>density functions</subject><subject>Derivation</subject><subject>Dynamical systems</subject><subject>Electrical Engineering, Electronic Engineering, Information Engineering</subject><subject>Elektroteknik och elektronik</subject><subject>Engineering and Technology</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>input-to-state stability</subject><subject>Lyapunov method</subject><subject>Lyapunov methods</subject><subject>Modelling and identification</subject><subject>Noise</subject><subject>Nonlinear dynamics</subject><subject>Observers</subject><subject>Physics</subject><subject>Reglerteknik</subject><subject>Rotational</subject><subject>Solid dynamics (ballistics, collision, multibody system, stabilization...)</subject><subject>Solid mechanics</subject><subject>Stability</subject><subject>Stability criteria</subject><subject>Teknik</subject><subject>Trajectory</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><sourceid>D8T</sourceid><recordid>eNpdkUuLFDEUhYMo2M64F9wUgriqnty8sxxaR4UWh3FchySVQIbqSlmpUvrfm7KbXri45PWdc8M9CL0BvAXA-ubxdrclGGBLgFCi8TO0Ac5VSzihz9EGY1CtJkq8RK9KeapHwRhs0P0uH1wa7Jzy0OTY7I92XIb8u7FD13wMQ0nzsblbBr8CpYl5an7M1qV-va_8Q57_aW3ffMvr5hq9iLYv4fV5vUI_7z497r60---fv-5u961nSs6tlkIH7RR00Xpno3A-EOlY9LqLWDkACdIq6QlnHRDFreOea8cjkxhTRq_Q_uRb_oRxcWac0sFOR5NtMv0y1nK1TAlGEsqY6jqjNHDDSMeMtUIaDLx2igqikNXuw8lunPKvJZTZHFLxoe_tEPJSjBZUEwC9Nn73H_mUl6kOoEJ1qnX2lFQInyA_5VKmEC__A2zWvEzNy6x5mXNeVfL-7GuLt32c7OBTueiIYJhRJSr39sSlEMLlmUvCQXD6F31VnLE</recordid><startdate>20111101</startdate><enddate>20111101</enddate><creator>Fernandes Vasconcelos, José</creator><creator>Rantzer, Anders</creator><creator>Silvestre, C.</creator><creator>Oliveira, P. J.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>ADTPV</scope><scope>AGCHP</scope><scope>AOWAS</scope><scope>D8T</scope><scope>D95</scope><scope>ZZAVC</scope></search><sort><creationdate>20111101</creationdate><title>Combination of Lyapunov and Density Functions for Stability of Rotational Motion</title><author>Fernandes Vasconcelos, José ; Rantzer, Anders ; Silvestre, C. ; Oliveira, P. J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c487t-9769e9b81dfacbaf6bce27b4fc9df08b11717a87c254d1285ab5c59b5f4700343</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Angular velocity</topic><topic>Applied sciences</topic><topic>Asymptotic stability</topic><topic>Computer science; control theory; systems</topic><topic>Control Engineering</topic><topic>Control system analysis</topic><topic>Control theory. Systems</topic><topic>Density</topic><topic>Density functional theory</topic><topic>density functions</topic><topic>Derivation</topic><topic>Dynamical systems</topic><topic>Electrical Engineering, Electronic Engineering, Information Engineering</topic><topic>Elektroteknik och elektronik</topic><topic>Engineering and Technology</topic><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>input-to-state stability</topic><topic>Lyapunov method</topic><topic>Lyapunov methods</topic><topic>Modelling and identification</topic><topic>Noise</topic><topic>Nonlinear dynamics</topic><topic>Observers</topic><topic>Physics</topic><topic>Reglerteknik</topic><topic>Rotational</topic><topic>Solid dynamics (ballistics, collision, multibody system, stabilization...)</topic><topic>Solid mechanics</topic><topic>Stability</topic><topic>Stability criteria</topic><topic>Teknik</topic><topic>Trajectory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fernandes Vasconcelos, José</creatorcontrib><creatorcontrib>Rantzer, Anders</creatorcontrib><creatorcontrib>Silvestre, C.</creatorcontrib><creatorcontrib>Oliveira, P. J.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><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>ANTE: Abstracts in New Technology & Engineering</collection><collection>SwePub</collection><collection>SWEPUB Lunds universitet full text</collection><collection>SwePub Articles</collection><collection>SWEPUB Freely available online</collection><collection>SWEPUB Lunds universitet</collection><collection>SwePub Articles full text</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Fernandes Vasconcelos, José</au><au>Rantzer, Anders</au><au>Silvestre, C.</au><au>Oliveira, P. J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Combination of Lyapunov and Density Functions for Stability of Rotational Motion</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2011-11-01</date><risdate>2011</risdate><volume>56</volume><issue>11</issue><spage>2599</spage><epage>2607</epage><pages>2599-2607</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>Lyapunov methods and density functions provide dual characterizations of the solutions of a nonlinear dynamic system. This work exploits the idea of combining both techniques, to yield stability results that are valid for almost all the solutions of the system. Based on the combination of Lyapunov and density functions, analysis methods are proposed for the derivation of almost input-to-state stability, and of almost global stability in nonlinear systems. The techniques are illustrated for an inertial attitude observer, where angular velocity readings are corrupted by non-idealities.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TAC.2011.2123290</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9286 |
| ispartof | IEEE transactions on automatic control, 2011-11, Vol.56 (11), p.2599-2607 |
| issn | 0018-9286 1558-2523 |
| language | eng |
| recordid | cdi_proquest_journals_901632932 |
| source | IEEE Electronic Library (IEL) |
| subjects | Angular velocity Applied sciences Asymptotic stability Computer science control theory systems Control Engineering Control system analysis Control theory. Systems Density Density functional theory density functions Derivation Dynamical systems Electrical Engineering, Electronic Engineering, Information Engineering Elektroteknik och elektronik Engineering and Technology Exact sciences and technology Fundamental areas of phenomenology (including applications) input-to-state stability Lyapunov method Lyapunov methods Modelling and identification Noise Nonlinear dynamics Observers Physics Reglerteknik Rotational Solid dynamics (ballistics, collision, multibody system, stabilization...) Solid mechanics Stability Stability criteria Teknik Trajectory |
| title | Combination of Lyapunov and Density Functions for Stability of Rotational Motion |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-02T09%3A50%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Combination%20of%20Lyapunov%20and%20Density%20Functions%20for%20Stability%20of%20Rotational%20Motion&rft.jtitle=IEEE%20transactions%20on%20automatic%20control&rft.au=Fernandes%20Vasconcelos,%20Jose%CC%81&rft.date=2011-11-01&rft.volume=56&rft.issue=11&rft.spage=2599&rft.epage=2607&rft.pages=2599-2607&rft.issn=0018-9286&rft.eissn=1558-2523&rft.coden=IETAA9&rft_id=info:doi/10.1109/TAC.2011.2123290&rft_dat=%3Cproquest_RIE%3E963921194%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=901632932&rft_id=info:pmid/&rft_ieee_id=5725165&rfr_iscdi=true |