{"id":"https://openalex.org/W2095406035","doi":"https://doi.org/10.1109/cdc.2008.4738982","title":"A Lyapunov-based small-gain theorem for hybrid ISS systems","display_name":"A Lyapunov-based small-gain theorem for hybrid ISS systems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2095406035","doi":"https://doi.org/10.1109/cdc.2008.4738982","mag":"2095406035"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4738982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-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":null,"display_name":"D. Nesic","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"D. Nesic","raw_affiliation_strings":["Department of Electrical and Electronics, University of Melbourne, Parkville, VIC, Australia","Dept. of Electr. & Electron., Univ. of Melbourne, Parkville, VIC, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronics, University of Melbourne, Parkville, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Dept. of Electr. & Electron., Univ. of Melbourne, Parkville, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002737786","display_name":"Andrew R. Teel","orcid":"https://orcid.org/0000-0002-6508-0879"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A.R. Teel","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","Electr. & Comput. Eng. Dept., Univ. of California in Santa Babara, Santa Babara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Electr. & Comput. Eng. Dept., Univ. of California in Santa Babara, Santa Babara, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":9.1344,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.97576445,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"3380","last_page":"3385"},"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":0.9987999796867371,"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":0.9987999796867371,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9951000213623047,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9948999881744385,"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":0.7626813650131226},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7275781035423279},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5960109233856201},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.5787221193313599},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5340219140052795},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.5299980044364929},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.440862774848938},{"id":"https://openalex.org/keywords/reset","display_name":"Reset (finance)","score":0.4321577250957489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4299051761627197},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4190014898777008},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3542966842651367},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33517318964004517},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.1709146499633789},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1433928906917572},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07401108741760254}],"concepts":[{"id":"https://openalex.org/C27385263","wikidata":"https://www.wikidata.org/wiki/Q4165677","display_name":"Small-gain theorem","level":3,"score":0.7626813650131226},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7275781035423279},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5960109233856201},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.5787221193313599},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5340219140052795},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.5299980044364929},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.440862774848938},{"id":"https://openalex.org/C2779795794","wikidata":"https://www.wikidata.org/wiki/Q7315343","display_name":"Reset (finance)","level":2,"score":0.4321577250957489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4299051761627197},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4190014898777008},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3542966842651367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33517318964004517},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.1709146499633789},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1433928906917572},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07401108741760254},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2008.4738982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1481510477","https://openalex.org/W1487112583","https://openalex.org/W1551360398","https://openalex.org/W1990502710","https://openalex.org/W2011105296","https://openalex.org/W2017493230","https://openalex.org/W2020711750","https://openalex.org/W2026769037","https://openalex.org/W2036826525","https://openalex.org/W2038137192","https://openalex.org/W2044100760","https://openalex.org/W2045945087","https://openalex.org/W2052123991","https://openalex.org/W2088680241","https://openalex.org/W2091357233","https://openalex.org/W2098989671","https://openalex.org/W2103254708","https://openalex.org/W2112248103","https://openalex.org/W2114241126","https://openalex.org/W2119655398","https://openalex.org/W2129792111","https://openalex.org/W2153570818","https://openalex.org/W2159479095","https://openalex.org/W2161213597","https://openalex.org/W2162750481","https://openalex.org/W4205940976","https://openalex.org/W6682653835"],"related_works":["https://openalex.org/W2383986032","https://openalex.org/W2534107666","https://openalex.org/W2349796700","https://openalex.org/W1975178315","https://openalex.org/W3217133416","https://openalex.org/W3194517843","https://openalex.org/W2620928602","https://openalex.org/W2098989671","https://openalex.org/W4376456722","https://openalex.org/W1588802810"],"abstract_inverted_index":{"A":[0],"Lyapunov-based":[1],"small-gain":[2,17],"theorem":[3],"is":[4],"presented":[5,40],"for":[6,19],"hybrid":[7],"systems":[8,23,35,38],"modelled":[9],"using":[10],"a":[11,54],"recently":[12],"proposed":[13],"framework":[14],"[9].":[15],"Lyapunov":[16],"theorems":[18],"continuous-time":[20],"and":[21,36,50],"discrete-time":[22],"are":[24,39,48],"special":[25],"cases":[26],"of":[27,56],"our":[28,43],"result.":[29,45],"Several":[30],"examples":[31],"including":[32],"networked":[33],"control":[34],"reset":[37],"to":[41,53],"illustrate":[42],"main":[44],"Our":[46],"results":[47],"general":[49],"they":[51],"apply":[52],"range":[55],"other":[57],"situations.":[58]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":10}],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2025-10-10T00:00:00"}