A Graphical Approach to Prove Contraction of Nonlinear Circuits and Systems
This paper derives a novel approach to prove contraction of nonlinear dynamical systems, based on the use of non-Euclidean norms and their associated matrix measures. A graphical procedure is developed to derive conditions for a system to be contracting. Such conditions can also be used to design co...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2011-02, Vol.58 (2), p.336-348 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 348 |
|---|---|
| container_issue | 2 |
| container_start_page | 336 |
| container_title | IEEE transactions on circuits and systems. I, Regular papers |
| container_volume | 58 |
| creator | Russo, G di Bernardo, M Slotine, J E |
| description | This paper derives a novel approach to prove contraction of nonlinear dynamical systems, based on the use of non-Euclidean norms and their associated matrix measures. A graphical procedure is developed to derive conditions for a system to be contracting. Such conditions can also be used to design control strategies to make a system contracting, or to design consensus and synchronization strategies for networks of nonlinear oscillators. After presenting the main steps of the approach and its proof, both for continuous-time and discrete-time systems, we illustrate the theoretical derivations on a set of representative examples. |
| doi_str_mv | 10.1109/TCSI.2010.2071810 |
| format | Article |
| fullrecord | <record><control><sourceid>crossref_RIE</sourceid><recordid>TN_cdi_crossref_primary_10_1109_TCSI_2010_2071810</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>5613961</ieee_id><sourcerecordid>10_1109_TCSI_2010_2071810</sourcerecordid><originalsourceid>FETCH-LOGICAL-c265t-ad6c04b1ed1c5c651f2eadc41a90e1bb792073ef644cf8833dc61f5bb8ffb2743</originalsourceid><addsrcrecordid>eNo9kFFLwzAUhYMoOKc_QHzJH-i8N2my9HEU3YZDhc3nkqYJi2xNSaqwf2_Lhg-Xcw-cc-F-hDwizBCheN6V2_WMwWAZzFEhXJEJCqEyUCCvxz0vMsWZuiV3KX0DsAI4Tsjbgi6j7vbe6ANddF0M2uxpH-hnDL-WlqHtoza9Dy0Njr6H9uBbqyMtfTQ_vk9Utw3dnlJvj-me3Dh9SPbholPy9fqyK1fZ5mO5LhebzDAp-kw30kBeo23QCCMFOmZ1Y3LUBVis63kxvMCtk3lunFKcN0aiE3WtnKvZPOdTgue7JoaUonVVF_1Rx1OFUI00qpFGNdKoLjSGztO54621_3khkRfD_AHmgFw-</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A Graphical Approach to Prove Contraction of Nonlinear Circuits and Systems</title><source>IEEE Electronic Library (IEL)</source><creator>Russo, G ; di Bernardo, M ; Slotine, J E</creator><creatorcontrib>Russo, G ; di Bernardo, M ; Slotine, J E</creatorcontrib><description>This paper derives a novel approach to prove contraction of nonlinear dynamical systems, based on the use of non-Euclidean norms and their associated matrix measures. A graphical procedure is developed to derive conditions for a system to be contracting. Such conditions can also be used to design control strategies to make a system contracting, or to design consensus and synchronization strategies for networks of nonlinear oscillators. After presenting the main steps of the approach and its proof, both for continuous-time and discrete-time systems, we illustrate the theoretical derivations on a set of representative examples.</description><identifier>ISSN: 1549-8328</identifier><identifier>EISSN: 1558-0806</identifier><identifier>DOI: 10.1109/TCSI.2010.2071810</identifier><identifier>CODEN: ITCSCH</identifier><language>eng</language><publisher>IEEE</publisher><subject>Atmospheric measurements ; Biological systems ; Convergence ; discrete-time systems ; Jacobian matrices ; nonlinear dynamical systems ; nonlinear network analysis ; Particle measurements ; Synchronization ; systems analysis and design ; Trajectory</subject><ispartof>IEEE transactions on circuits and systems. I, Regular papers, 2011-02, Vol.58 (2), p.336-348</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c265t-ad6c04b1ed1c5c651f2eadc41a90e1bb792073ef644cf8833dc61f5bb8ffb2743</citedby><cites>FETCH-LOGICAL-c265t-ad6c04b1ed1c5c651f2eadc41a90e1bb792073ef644cf8833dc61f5bb8ffb2743</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/5613961$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/5613961$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Russo, G</creatorcontrib><creatorcontrib>di Bernardo, M</creatorcontrib><creatorcontrib>Slotine, J E</creatorcontrib><title>A Graphical Approach to Prove Contraction of Nonlinear Circuits and Systems</title><title>IEEE transactions on circuits and systems. I, Regular papers</title><addtitle>TCSI</addtitle><description>This paper derives a novel approach to prove contraction of nonlinear dynamical systems, based on the use of non-Euclidean norms and their associated matrix measures. A graphical procedure is developed to derive conditions for a system to be contracting. Such conditions can also be used to design control strategies to make a system contracting, or to design consensus and synchronization strategies for networks of nonlinear oscillators. After presenting the main steps of the approach and its proof, both for continuous-time and discrete-time systems, we illustrate the theoretical derivations on a set of representative examples.</description><subject>Atmospheric measurements</subject><subject>Biological systems</subject><subject>Convergence</subject><subject>discrete-time systems</subject><subject>Jacobian matrices</subject><subject>nonlinear dynamical systems</subject><subject>nonlinear network analysis</subject><subject>Particle measurements</subject><subject>Synchronization</subject><subject>systems analysis and design</subject><subject>Trajectory</subject><issn>1549-8328</issn><issn>1558-0806</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kFFLwzAUhYMoOKc_QHzJH-i8N2my9HEU3YZDhc3nkqYJi2xNSaqwf2_Lhg-Xcw-cc-F-hDwizBCheN6V2_WMwWAZzFEhXJEJCqEyUCCvxz0vMsWZuiV3KX0DsAI4Tsjbgi6j7vbe6ANddF0M2uxpH-hnDL-WlqHtoza9Dy0Njr6H9uBbqyMtfTQ_vk9Utw3dnlJvj-me3Dh9SPbholPy9fqyK1fZ5mO5LhebzDAp-kw30kBeo23QCCMFOmZ1Y3LUBVis63kxvMCtk3lunFKcN0aiE3WtnKvZPOdTgue7JoaUonVVF_1Rx1OFUI00qpFGNdKoLjSGztO54621_3khkRfD_AHmgFw-</recordid><startdate>20110201</startdate><enddate>20110201</enddate><creator>Russo, G</creator><creator>di Bernardo, M</creator><creator>Slotine, J E</creator><general>IEEE</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20110201</creationdate><title>A Graphical Approach to Prove Contraction of Nonlinear Circuits and Systems</title><author>Russo, G ; di Bernardo, M ; Slotine, J E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c265t-ad6c04b1ed1c5c651f2eadc41a90e1bb792073ef644cf8833dc61f5bb8ffb2743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Atmospheric measurements</topic><topic>Biological systems</topic><topic>Convergence</topic><topic>discrete-time systems</topic><topic>Jacobian matrices</topic><topic>nonlinear dynamical systems</topic><topic>nonlinear network analysis</topic><topic>Particle measurements</topic><topic>Synchronization</topic><topic>systems analysis and design</topic><topic>Trajectory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Russo, G</creatorcontrib><creatorcontrib>di Bernardo, M</creatorcontrib><creatorcontrib>Slotine, J E</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>CrossRef</collection><jtitle>IEEE transactions on circuits and systems. I, Regular papers</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Russo, G</au><au>di Bernardo, M</au><au>Slotine, J E</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Graphical Approach to Prove Contraction of Nonlinear Circuits and Systems</atitle><jtitle>IEEE transactions on circuits and systems. I, Regular papers</jtitle><stitle>TCSI</stitle><date>2011-02-01</date><risdate>2011</risdate><volume>58</volume><issue>2</issue><spage>336</spage><epage>348</epage><pages>336-348</pages><issn>1549-8328</issn><eissn>1558-0806</eissn><coden>ITCSCH</coden><abstract>This paper derives a novel approach to prove contraction of nonlinear dynamical systems, based on the use of non-Euclidean norms and their associated matrix measures. A graphical procedure is developed to derive conditions for a system to be contracting. Such conditions can also be used to design control strategies to make a system contracting, or to design consensus and synchronization strategies for networks of nonlinear oscillators. After presenting the main steps of the approach and its proof, both for continuous-time and discrete-time systems, we illustrate the theoretical derivations on a set of representative examples.</abstract><pub>IEEE</pub><doi>10.1109/TCSI.2010.2071810</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 1549-8328 |
| ispartof | IEEE transactions on circuits and systems. I, Regular papers, 2011-02, Vol.58 (2), p.336-348 |
| issn | 1549-8328 1558-0806 |
| language | eng |
| recordid | cdi_crossref_primary_10_1109_TCSI_2010_2071810 |
| source | IEEE Electronic Library (IEL) |
| subjects | Atmospheric measurements Biological systems Convergence discrete-time systems Jacobian matrices nonlinear dynamical systems nonlinear network analysis Particle measurements Synchronization systems analysis and design Trajectory |
| title | A Graphical Approach to Prove Contraction of Nonlinear Circuits and Systems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-09T18%3A16%3A03IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Graphical%20Approach%20to%20Prove%20Contraction%20of%20Nonlinear%20Circuits%20and%20Systems&rft.jtitle=IEEE%20transactions%20on%20circuits%20and%20systems.%20I,%20Regular%20papers&rft.au=Russo,%20G&rft.date=2011-02-01&rft.volume=58&rft.issue=2&rft.spage=336&rft.epage=348&rft.pages=336-348&rft.issn=1549-8328&rft.eissn=1558-0806&rft.coden=ITCSCH&rft_id=info:doi/10.1109/TCSI.2010.2071810&rft_dat=%3Ccrossref_RIE%3E10_1109_TCSI_2010_2071810%3C/crossref_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_ieee_id=5613961&rfr_iscdi=true |