{"id":"https://openalex.org/W4409152690","doi":"https://doi.org/10.1109/tac.2025.3558142","title":"An LMI Formulation of Small-Gain Theorems for 2-Contraction of Nonlinear Interconnected Systems","display_name":"An LMI Formulation of Small-Gain Theorems for 2-Contraction of Nonlinear Interconnected Systems","publication_year":2025,"publication_date":"2025-04-04","ids":{"openalex":"https://openalex.org/W4409152690","doi":"https://doi.org/10.1109/tac.2025.3558142"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3558142","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3558142","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","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/A5037354850","display_name":"David Angeli","orcid":"https://orcid.org/0000-0002-5311-4306"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"David Angeli","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043281950","display_name":"Davide Martini","orcid":null},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Davide Martini","raw_affiliation_strings":["Department of Information Engineering, University of Florence, Firenze, Italy","Dept of Information Engineering, University of Florence, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Information Engineering, University of Florence, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dept of Information Engineering, University of Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078497169","display_name":"Giacomo Innocenti","orcid":"https://orcid.org/0000-0002-2110-826X"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giacomo Innocenti","raw_affiliation_strings":["Department of Information Engineering, University of Florence, Firenze, Italy","Dept of Information Engineering, University of Florence, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Information Engineering, University of Florence, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dept of Information Engineering, University of Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074942219","display_name":"A. Tesi","orcid":"https://orcid.org/0000-0002-0234-5999"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Tesi","raw_affiliation_strings":["Department of Information Engineering, University of Florence, Firenze, Italy","Dept of Information Engineering, University of Florence, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Information Engineering, University of Florence, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dept of Information Engineering, University of Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037354850"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":3.6475,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.92110471,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"70","issue":"9","first_page":"6214","last_page":"6221"},"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":0.9986000061035156,"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":0.9986000061035156,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9391999840736389,"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":0.6592562794685364},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6371445655822754},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6208631992340088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5129455924034119},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3464829921722412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3250194787979126},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18554753065109253},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11809772253036499},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06041368842124939},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.04440188407897949}],"concepts":[{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.6592562794685364},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6371445655822754},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6208631992340088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5129455924034119},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3464829921722412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3250194787979126},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18554753065109253},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11809772253036499},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06041368842124939},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.04440188407897949},{"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/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2025.3558142","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3558142","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/1424748","is_oa":false,"landing_page_url":"https://hdl.handle.net/2158/1424748","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1517248966","https://openalex.org/W1563289057","https://openalex.org/W1965567178","https://openalex.org/W1994003949","https://openalex.org/W1998967624","https://openalex.org/W2008663032","https://openalex.org/W2036216368","https://openalex.org/W2036826525","https://openalex.org/W2084643110","https://openalex.org/W2117079884","https://openalex.org/W2120939156","https://openalex.org/W2134889984","https://openalex.org/W2241556088","https://openalex.org/W2476238858","https://openalex.org/W2532721651","https://openalex.org/W3162230888","https://openalex.org/W3195167977","https://openalex.org/W3214804586","https://openalex.org/W4210452658","https://openalex.org/W4220903325","https://openalex.org/W4285151295","https://openalex.org/W4293104639","https://openalex.org/W4388918216"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"small-gain":[3],"sufficient":[4],"conditions":[5],"for":[6],"2-contraction":[7],"of":[8,15,18,26,41,64,85,89],"feedback":[9],"interconnected":[10],"systems,":[11],"on":[12],"the":[13,27,39,61,68,79],"basis":[14],"individual":[16,52],"gains":[17,35],"suitable":[19,42],"subsystems":[20,53],"arising":[21],"from":[22],"a":[23],"modular":[24],"decomposition":[25],"second":[28,69],"additive":[29,70],"compound":[30,71],"matrix":[31],"variational":[32],"equation.":[33],"The":[34,45],"are":[36],"computed":[37],"through":[38],"solution":[40],"LMI":[43],"conditions.":[44],"criterion":[46],"applies":[47],"even":[48],"to":[49,56,60,77],"cases":[50],"when":[51],"might":[54],"fail":[55],"be":[57],"contractive,":[58],"thanks":[59],"extra":[62],"margin":[63],"contraction":[65],"afforded":[66],"by":[67],"matrix.":[72],"One":[73],"example":[74],"is":[75],"provided":[76],"illustrate":[78],"theory":[80],"and":[81,87],"show":[82],"its":[83],"degree":[84],"conservatism":[86],"scope":[88],"applicability.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}