{"id":"https://openalex.org/W3136646910","doi":"https://doi.org/10.1109/cdc45484.2021.9683092","title":"Scaled relative graphs for system analysis","display_name":"Scaled relative graphs for system analysis","publication_year":2021,"publication_date":"2021-12-14","ids":{"openalex":"https://openalex.org/W3136646910","doi":"https://doi.org/10.1109/cdc45484.2021.9683092","mag":"3136646910"},"language":"en","primary_location":{"id":"doi:10.1109/cdc45484.2021.9683092","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683092","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 60th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.13971","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083646753","display_name":"Thomas Chaffey","orcid":"https://orcid.org/0000-0002-4131-6090"},"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":"Thomas Chaffey","raw_affiliation_strings":["University of Cambridge,Department of Engineering,Cambridge,CB2 1PZ","Univ. of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge,Department of Engineering,Cambridge,CB2 1PZ","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Univ. of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"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":"Fulvio Forni","raw_affiliation_strings":["University of Cambridge,Department of Engineering,Cambridge,CB2 1PZ","Univ. of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge,Department of Engineering,Cambridge,CB2 1PZ","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Univ. of Cambridge","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":"Rodolphe Sepulchre","raw_affiliation_strings":["University of Cambridge,Department of Engineering,Cambridge,CB2 1PZ","Univ. of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge,Department of Engineering,Cambridge,CB2 1PZ","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Univ. of Cambridge","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3166","last_page":"3172"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9965999722480774,"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/T11236","display_name":"Control Systems and Identification","score":0.9959999918937683,"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/euclidean-geometry","display_name":"Euclidean geometry","score":0.6009218096733093},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.5991363525390625},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5050373673439026},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5026202201843262},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4881168305873871},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4598155915737152},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4375944137573242},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4203718602657318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41630226373672485},{"id":"https://openalex.org/keywords/nyquist-plot","display_name":"Nyquist plot","score":0.41206544637680054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4104929566383362},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3938789963722229},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3278448283672333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13812369108200073}],"concepts":[{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6009218096733093},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5991363525390625},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5050373673439026},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5026202201843262},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4881168305873871},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4598155915737152},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4375944137573242},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4203718602657318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41630226373672485},{"id":"https://openalex.org/C195762429","wikidata":"https://www.wikidata.org/wiki/Q1756793","display_name":"Nyquist plot","level":5,"score":0.41206544637680054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4104929566383362},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3938789963722229},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3278448283672333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13812369108200073},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C52859227","wikidata":"https://www.wikidata.org/wiki/Q7877","display_name":"Electrochemistry","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C7040849","wikidata":"https://www.wikidata.org/wiki/Q899580","display_name":"Dielectric spectroscopy","level":4,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1109/cdc45484.2021.9683092","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683092","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 60th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2103.13971","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.13971","pdf_url":"https://arxiv.org/pdf/2103.13971","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/388367","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/388367","pdf_url":"https://www.repository.cam.ac.uk/bitstreams/b82cac08-59f6-4ec6-8fd6-40ef6e5e4f2f/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"mag:3136646910","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2103.13971.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:generic.eprints.org:1284625","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/1284625/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.2103.13971","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.13971","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.17863/cam.120761","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.120761","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.13971","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.13971","pdf_url":"https://arxiv.org/pdf/2103.13971","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3136646910.pdf","grobid_xml":"https://content.openalex.org/works/W3136646910.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W597526370","https://openalex.org/W658292533","https://openalex.org/W1487127700","https://openalex.org/W1530136772","https://openalex.org/W2026769037","https://openalex.org/W2047645385","https://openalex.org/W2097944741","https://openalex.org/W2132185311","https://openalex.org/W2144355672","https://openalex.org/W2166182757","https://openalex.org/W2916081703","https://openalex.org/W3024233472","https://openalex.org/W4253695808","https://openalex.org/W6772446426","https://openalex.org/W6786935366","https://openalex.org/W6799268607"],"related_works":["https://openalex.org/W2082517528","https://openalex.org/W2790984073","https://openalex.org/W2804121567","https://openalex.org/W2083104277","https://openalex.org/W3102749021","https://openalex.org/W3010501116","https://openalex.org/W2294115529","https://openalex.org/W2091647203","https://openalex.org/W2064062413","https://openalex.org/W2130096835","https://openalex.org/W2054640515","https://openalex.org/W2135441544","https://openalex.org/W1977690592","https://openalex.org/W3098574429","https://openalex.org/W3119949288","https://openalex.org/W2887927994","https://openalex.org/W2996807429","https://openalex.org/W3015809372","https://openalex.org/W2177414390","https://openalex.org/W2890911599"],"abstract_inverted_index":{"Scaled":[0],"relative":[1,24,56],"graphs":[2,25],"were":[3],"recently":[4],"introduced":[5],"to":[6,26,69,86,95,104],"analyze":[7],"the":[8,27,37,50,77,111],"convergence":[9],"of":[10,30,40,53,62,72,92,98,110],"optimization":[11],"algorithms":[12],"using":[13],"two":[14],"dimensional":[15],"Euclidean":[16],"geometry.":[17],"In":[18],"this":[19],"paper,":[20],"we":[21],"connect":[22],"scaled":[23,55],"classical":[28,112],"theory":[29],"input/output":[31],"systems.":[32],"It":[33],"is":[34,49,102],"shown":[35],"that":[36],"Nyquist":[38],"diagram":[39],"an":[41],"LTI":[42],"system":[43,84],"on":[44],"L":[45],"<inf":[46],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[47],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>":[48],"convex":[51],"hull":[52],"its":[54],"graph":[57],"under":[58],"a":[59,106],"particular":[60],"change":[61],"coordinates.":[63],"The":[64],"SRG":[65],"may":[66],"be":[67,87],"used":[68,103],"visualize":[70],"approximations":[71],"static":[73],"nonlinearities":[74],"such":[75],"as":[76],"describing":[78],"function":[79],"and":[80],"quadratic":[81],"constraints,":[82],"allowing":[83],"properties":[85],"verified":[88],"or":[89],"disproved.":[90],"Interconnections":[91],"systems":[93],"correspond":[94],"graphical":[96,108],"manipulations":[97],"their":[99],"SRGs.":[100],"This":[101],"provide":[105],"simple,":[107],"proof":[109],"incremental":[113],"passivity":[114],"theorem.":[115]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}