{"id":"https://openalex.org/W2120939156","doi":"https://doi.org/10.1109/cdc.2013.6760821","title":"Transverse contraction criteria for existence, stability, and robustness of a limit cycle","display_name":"Transverse contraction criteria for existence, stability, and robustness of a limit cycle","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2120939156","doi":"https://doi.org/10.1109/cdc.2013.6760821","mag":"2120939156"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6760821","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026600708","display_name":"Ian R. Manchester","orcid":"https://orcid.org/0000-0002-7035-3173"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Ian R. Manchester","raw_affiliation_strings":["ACFR, University of Sydney, Australia","Sch. of Aerosp., Univ. of Sydney, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"ACFR, University of Sydney, Australia","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"Sch. of Aerosp., Univ. of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044026747","display_name":"Jean-Jacques Slotine","orcid":"https://orcid.org/0000-0002-7161-7812"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean-Jacques E. Slotine","raw_affiliation_strings":["Nonlinear Systems Laboratory, Massachusetts Institute of Technology, USA","Nonlinear Syst. Lab. Massachusetts, Inst. of Technol., Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Nonlinear Systems Laboratory, Massachusetts Institute of Technology, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Nonlinear Syst. Lab. Massachusetts, Inst. of Technol., Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026600708"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":null,"apc_paid":null,"fwci":3.5601,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.92956183,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"5909","last_page":"5914"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12763","display_name":"ATP Synthase and ATPases Research","score":0.968500018119812,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9555000066757202,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.7745547294616699},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6041019558906555},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5760576128959656},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5570846796035767},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.48942509293556213},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4552551209926605},{"id":"https://openalex.org/keywords/transverse-plane","display_name":"Transverse plane","score":0.4521482288837433},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.4385952055454254},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41727474331855774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3617154359817505},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3385070860385895},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.271157830953598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22445958852767944},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.06865864992141724},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06730562448501587}],"concepts":[{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.7745547294616699},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6041019558906555},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5760576128959656},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5570846796035767},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.48942509293556213},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4552551209926605},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.4521482288837433},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.4385952055454254},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41727474331855774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3617154359817505},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3385070860385895},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.271157830953598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22445958852767944},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06865864992141724},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06730562448501587},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2013.6760821","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.762.383","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.762.383","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1209.4433.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W335071387","https://openalex.org/W1499319316","https://openalex.org/W1541665771","https://openalex.org/W1548118198","https://openalex.org/W1669291173","https://openalex.org/W1967184028","https://openalex.org/W1981717790","https://openalex.org/W1997411276","https://openalex.org/W2022781970","https://openalex.org/W2026036461","https://openalex.org/W2026769037","https://openalex.org/W2033118636","https://openalex.org/W2043009207","https://openalex.org/W2043810922","https://openalex.org/W2046314965","https://openalex.org/W2046337985","https://openalex.org/W2046472465","https://openalex.org/W2074697762","https://openalex.org/W2079521041","https://openalex.org/W2090167557","https://openalex.org/W2097944741","https://openalex.org/W2104730516","https://openalex.org/W2106985815","https://openalex.org/W2112406447","https://openalex.org/W2119491087","https://openalex.org/W2129644659","https://openalex.org/W2134889984","https://openalex.org/W2135234927","https://openalex.org/W2136384363","https://openalex.org/W2151265887","https://openalex.org/W2165861322","https://openalex.org/W2167412190","https://openalex.org/W2174809691","https://openalex.org/W2178904312","https://openalex.org/W2320012146","https://openalex.org/W2322760626","https://openalex.org/W2360806034","https://openalex.org/W2404700831","https://openalex.org/W2951081417","https://openalex.org/W2963075264","https://openalex.org/W2963186291","https://openalex.org/W3034208633","https://openalex.org/W3098955748","https://openalex.org/W3117723976","https://openalex.org/W4230748309","https://openalex.org/W4232854299","https://openalex.org/W4253134649","https://openalex.org/W4298358998","https://openalex.org/W4300433886","https://openalex.org/W6632410300","https://openalex.org/W6637188559","https://openalex.org/W6670489864","https://openalex.org/W6824097804"],"related_works":["https://openalex.org/W143502885","https://openalex.org/W42113618","https://openalex.org/W2103468410","https://openalex.org/W2480115405","https://openalex.org/W3197542402","https://openalex.org/W1856228368","https://openalex.org/W2971527398","https://openalex.org/W82829784","https://openalex.org/W1929207905","https://openalex.org/W1025150868"],"abstract_inverted_index":{"This":[0,19],"paper":[1],"derives":[2],"a":[3,27,53,73],"differential":[4,85,89],"contraction":[5,21,71,91,94],"condition":[6,22],"for":[7,47,98],"the":[8,50,82],"existence":[9,51],"of":[10,49,52,60,70,76,84],"an":[11,16],"orbitally-stable":[12],"limit":[13,55],"cycle":[14],"in":[15],"autonomous":[17],"system.":[18],"transverse":[20,88,93],"can":[23,95],"be":[24,43,96],"represented":[25],"as":[26,39],"pointwise":[28],"linear":[29],"matrix":[30],"inequality":[31],"(LMI),":[32],"thus":[33],"allowing":[34],"convex":[35],"optimization":[36],"tools":[37],"such":[38],"sum-of-squares":[40],"programming":[41],"to":[42,45,65],"used":[44],"search":[46],"certificates":[48],"stable":[54],"cycle.":[56],"Many":[57],"desirable":[58],"properties":[59],"contracting":[61],"dynamics":[62],"are":[63],"extended":[64],"this":[66],"context,":[67],"including":[68],"preservation":[69],"under":[72],"broad":[74],"class":[75],"interconnections.":[77],"In":[78],"addition,":[79],"by":[80],"introducing":[81],"concepts":[83],"dissipativity":[86],"and":[87,92],"dissipativity,":[90],"established":[97],"large":[99],"scale":[100],"systems":[101],"via":[102],"LMI":[103],"conditions":[104],"on":[105],"component":[106],"subsystems.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
