{"id":"https://openalex.org/W2108912872","doi":"https://doi.org/10.1109/tac.2013.2286898","title":"A Small-Gain Theorem for Switched Interconnected Nonlinear Systems and Its Applications","display_name":"A Small-Gain Theorem for Switched Interconnected Nonlinear Systems and Its Applications","publication_year":2013,"publication_date":"2013-10-23","ids":{"openalex":"https://openalex.org/W2108912872","doi":"https://doi.org/10.1109/tac.2013.2286898","mag":"2108912872"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2286898","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2286898","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/A5027939945","display_name":"Lijun Long","orcid":"https://orcid.org/0000-0003-2950-2410"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lijun Long","raw_affiliation_strings":["Northeastern University, State Key Laboratory of Synthetical Automation for Process Industries, Shenyang, P. R. China","State Key Lab. of Synthetical Autom. for Process Ind., Northeastern Univ., Shenyang, China"],"affiliations":[{"raw_affiliation_string":"Northeastern University, State Key Laboratory of Synthetical Automation for Process Industries, Shenyang, P. R. China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"State Key Lab. of Synthetical Autom. for Process Ind., Northeastern Univ., Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100358003","display_name":"Jun Zhao","orcid":"https://orcid.org/0000-0001-9096-103X"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Zhao","raw_affiliation_strings":["Northeastern University, State Key Laboratory of Synthetical Automation for Process Industries, Shenyang, P. R. China","State Key Lab. of Synthetical Autom. for Process Ind., Northeastern Univ., Shenyang, China"],"affiliations":[{"raw_affiliation_string":"Northeastern University, State Key Laboratory of Synthetical Automation for Process Industries, Shenyang, P. R. China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"State Key Lab. of Synthetical Autom. for Process Ind., Northeastern Univ., Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027939945"],"corresponding_institution_ids":["https://openalex.org/I9224756"],"apc_list":null,"apc_paid":null,"fwci":20.7034,"has_fulltext":false,"cited_by_count":128,"citation_normalized_percentile":{"value":0.99480984,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"59","issue":"4","first_page":"1082","last_page":"1088"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain 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/T10046","display_name":"Stability and Control of Uncertain 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":0.9976000189781189,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9970999956130981,"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/small-gain-theorem","display_name":"Small-gain theorem","score":0.8647436499595642},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7722728252410889},{"id":"https://openalex.org/keywords/dwell-time","display_name":"Dwell time","score":0.767041027545929},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7530962228775024},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.54183030128479},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5046180486679077},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45187896490097046},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4229559004306793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3963339626789093},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.34299221634864807},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08631709218025208},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06700578331947327},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06060168147087097}],"concepts":[{"id":"https://openalex.org/C27385263","wikidata":"https://www.wikidata.org/wiki/Q4165677","display_name":"Small-gain theorem","level":3,"score":0.8647436499595642},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7722728252410889},{"id":"https://openalex.org/C151637689","wikidata":"https://www.wikidata.org/wiki/Q5318064","display_name":"Dwell time","level":2,"score":0.767041027545929},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7530962228775024},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.54183030128479},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5046180486679077},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45187896490097046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4229559004306793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3963339626789093},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.34299221634864807},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08631709218025208},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06700578331947327},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06060168147087097},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C70410870","wikidata":"https://www.wikidata.org/wiki/Q199906","display_name":"Clinical psychology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2013.2286898","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2286898","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W94675972","https://openalex.org/W579832045","https://openalex.org/W1487112583","https://openalex.org/W1552094772","https://openalex.org/W1900371862","https://openalex.org/W1976440798","https://openalex.org/W1996505464","https://openalex.org/W2001967263","https://openalex.org/W2006862199","https://openalex.org/W2008151824","https://openalex.org/W2033505412","https://openalex.org/W2036120594","https://openalex.org/W2036826525","https://openalex.org/W2062974796","https://openalex.org/W2068259262","https://openalex.org/W2074857762","https://openalex.org/W2083575195","https://openalex.org/W2095040111","https://openalex.org/W2098898086","https://openalex.org/W2101452290","https://openalex.org/W2104480368","https://openalex.org/W2104840798","https://openalex.org/W2118741873","https://openalex.org/W2130169782","https://openalex.org/W2136603878","https://openalex.org/W2139422732","https://openalex.org/W2144355672","https://openalex.org/W2157564130","https://openalex.org/W2159130301","https://openalex.org/W2160503069","https://openalex.org/W2163344855","https://openalex.org/W2164441628","https://openalex.org/W2164818757","https://openalex.org/W2607614170","https://openalex.org/W3160954918","https://openalex.org/W4205940976","https://openalex.org/W4214690803","https://openalex.org/W6639670352"],"related_works":["https://openalex.org/W2898247383","https://openalex.org/W1977953789","https://openalex.org/W633869025","https://openalex.org/W4384341054","https://openalex.org/W2007903413","https://openalex.org/W2966405498","https://openalex.org/W2118385007","https://openalex.org/W4390507347","https://openalex.org/W2360858150","https://openalex.org/W370365947"],"abstract_inverted_index":{"A":[0,75],"small-gain":[1,40],"theorem":[2],"for":[3,15,78,99],"switched":[4,20,52,110],"interconnected":[5],"nonlinear":[6,53,111],"systems":[7,54],"is":[8,35,93,103],"set":[9],"up":[10],"which":[11],"provides":[12],"a":[13,23,84,107],"tool":[14],"analyzing":[16],"the":[17,31,39,46,79],"behavior":[18],"of":[19,48,51,86,109],"systems.":[21,114],"Also,":[22],"method":[24],"exploiting":[25],"an":[26],"average":[27,90],"dwell":[28,91],"time":[29,92],"and":[30,71],"small":[32],"gain":[33],"technique":[34],"proposed.":[36],"Based":[37],"on":[38],"theorem,":[41],"this":[42],"technical":[43],"note":[44],"investigates":[45],"problem":[47,82],"global":[49,80],"stabilization":[50,81],"in":[55],"strict-feedback":[56],"form":[57],"whose":[58],"all":[59],"zero":[60],"dynamics":[61],"are":[62,69,73],"input-to-state":[63],"stable":[64],"(ISS)":[65],"or":[66],"only":[67],"some":[68],"ISS":[70],"others":[72],"not.":[74],"sufficient":[76],"condition":[77],"under":[83],"class":[85,108],"switching":[87],"signals":[88],"with":[89],"derived":[94],"by":[95],"constructing":[96],"state-feedback":[97],"controllers":[98],"subsystems.":[100],"The":[101],"result":[102],"also":[104],"applied":[105],"to":[106],"network":[112],"control":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}