{"id":"https://openalex.org/W2964269893","doi":"https://doi.org/10.1109/cdc.2015.7403327","title":"An operator-theoretic approach to differential positivity","display_name":"An operator-theoretic approach to differential positivity","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2964269893","doi":"https://doi.org/10.1109/cdc.2015.7403327","mag":"2964269893"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7403327","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403327","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.repository.cam.ac.uk/bitstreams/87cdfacf-0604-4559-bd5a-e17dc13b8002/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019128476","display_name":"Alexandre Mauroy","orcid":"https://orcid.org/0000-0002-1594-4317"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"A. Mauroy","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Li&#x00E8;ge, 4000, Belgium","Universite de Liege, Liege, BE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Li&#x00E8;ge, 4000, Belgium","institution_ids":["https://openalex.org/I157674565"]},{"raw_affiliation_string":"Universite de Liege, Liege, BE","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034730197","display_name":"Fulvio Forni","orcid":"https://orcid.org/0000-0002-5728-0176"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"F. Forni","raw_affiliation_strings":["University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067642477","display_name":"Rodolphe Sepulchre","orcid":"https://orcid.org/0000-0002-7047-3124"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R. Sepulchre","raw_affiliation_strings":["University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"7028","last_page":"7033"},"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":0.9980999827384949,"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":0.9980999827384949,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9975000023841858,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9911999702453613,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6901217699050903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6804159283638},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6569908261299133},{"id":"https://openalex.org/keywords/positive-systems","display_name":"Positive systems","score":0.6302327513694763},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.6137959957122803},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6064044237136841},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5895795226097107},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5463148355484009},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4903836250305176},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47652706503868103},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39960867166519165},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2781863212585449},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.20020180940628052},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12123513221740723},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07570764422416687}],"concepts":[{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6901217699050903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6804159283638},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6569908261299133},{"id":"https://openalex.org/C2778299942","wikidata":"https://www.wikidata.org/wiki/Q7233296","display_name":"Positive systems","level":3,"score":0.6302327513694763},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.6137959957122803},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6064044237136841},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5895795226097107},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5463148355484009},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4903836250305176},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47652706503868103},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39960867166519165},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2781863212585449},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.20020180940628052},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12123513221740723},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07570764422416687},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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.2015.7403327","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403327","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/251264","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/251264","pdf_url":"https://www.repository.cam.ac.uk/bitstreams/87cdfacf-0604-4559-bd5a-e17dc13b8002/download","source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference Object"}],"best_oa_location":{"id":"pmh:oai:www.repository.cam.ac.uk:1810/251264","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/251264","pdf_url":"https://www.repository.cam.ac.uk/bitstreams/87cdfacf-0604-4559-bd5a-e17dc13b8002/download","source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference Object"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964269893.pdf","grobid_xml":"https://content.openalex.org/works/W2964269893.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1534430411","https://openalex.org/W1851248039","https://openalex.org/W2001462939","https://openalex.org/W2016315007","https://openalex.org/W2016358031","https://openalex.org/W2036216368","https://openalex.org/W2069159682","https://openalex.org/W2076598792","https://openalex.org/W2082042541","https://openalex.org/W2114876173","https://openalex.org/W2147741970","https://openalex.org/W2168132433","https://openalex.org/W2953330175","https://openalex.org/W3099674394"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2769269860","https://openalex.org/W2963377682","https://openalex.org/W2083968322","https://openalex.org/W2070724789","https://openalex.org/W4382985020","https://openalex.org/W1973339055","https://openalex.org/W2106609868","https://openalex.org/W3011950536"],"abstract_inverted_index":{"Differentially":[0],"positive":[1,52,81],"systems":[2,4,53],"are":[3],"whose":[5],"linearization":[6],"along":[7],"trajectories":[8],"is":[9,79],"positive.":[10],"Under":[11],"mild":[12],"assumptions,":[13],"their":[14],"solutions":[15],"asymptotically":[16],"converge":[17],"to":[18],"a":[19,25,93],"one-dimensional":[20],"attractor,":[21],"which":[22],"must":[23],"be":[24],"limit":[26,36,77],"cycle":[27,78],"in":[28,34,82],"the":[29,35,43,47,55,59,90],"absence":[30],"of":[31,50,58,85,92],"fixed":[32],"points":[33],"set.":[37],"In":[38,62],"this":[39],"paper,":[40],"we":[41,64],"investigate":[42],"general":[44],"connections":[45],"between":[46],"(geometric)":[48],"properties":[49,57],"differentially":[51,80],"and":[54],"(spectral)":[56],"Koopman":[60],"operator.":[61],"particular,":[63],"obtain":[65],"converse":[66],"results":[67],"for":[68,72],"differential":[69],"positivity,":[70],"showing":[71],"instance":[73],"that":[74],"any":[75],"hyperbolic":[76],"its":[83],"basin":[84],"attraction.":[86],"We":[87],"also":[88],"provide":[89],"construction":[91],"contracting":[94],"cone":[95],"field.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
