{"id":"https://openalex.org/W2602502146","doi":"https://doi.org/10.1137/090746483","title":"Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions","display_name":"Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2602502146","doi":"https://doi.org/10.1137/090746483","mag":"2602502146"},"language":"en","primary_location":{"id":"doi:10.1137/090746483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090746483","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0901.1842","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Sergey N. Dashkovskiy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sergey N. Dashkovskiy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Bj\u00f6rn S. R\u00fcffer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bj\u00f6rn S. R\u00fcffer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Fabian R. Wirth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fabian R. Wirth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":35.1877,"has_fulltext":false,"cited_by_count":340,"citation_normalized_percentile":{"value":0.99782193,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"48","issue":"6","first_page":"4089","last_page":"4118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.42250001430511475,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.42250001430511475,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.2101999968290329,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.17190000414848328,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7509999871253967},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7491000294685364},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.576200008392334},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.553600013256073},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5512999892234802},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5062999725341797},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5038999915122986},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.4867999851703644},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4819999933242798}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8452000021934509},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7509999871253967},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7491000294685364},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.576200008392334},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.553600013256073},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5512999892234802},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5062999725341797},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5038999915122986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49320000410079956},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.4867999851703644},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47510001063346863},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4408000111579895},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4259999990463257},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3986000120639801},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.3885999917984009},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.36149999499320984},{"id":"https://openalex.org/C27385263","wikidata":"https://www.wikidata.org/wiki/Q4165677","display_name":"Small-gain theorem","level":3,"score":0.33959999680519104},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.31310001015663147},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2825999855995178},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.25440001487731934},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090746483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090746483","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0901.1842","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.1842","pdf_url":"https://arxiv.org/pdf/0901.1842","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0901.1842","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.1842","pdf_url":"https://arxiv.org/pdf/0901.1842","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6563694554","display_name":null,"funder_award_id":"SFB 637","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1608548244","https://openalex.org/W1967464662","https://openalex.org/W1978108057","https://openalex.org/W1994003949","https://openalex.org/W2000599128","https://openalex.org/W2004470537","https://openalex.org/W2014549417","https://openalex.org/W2017493230","https://openalex.org/W2036826525","https://openalex.org/W2045945087","https://openalex.org/W2070994188","https://openalex.org/W2074857762","https://openalex.org/W2097908381","https://openalex.org/W2134078068","https://openalex.org/W2165626406"],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"interconnections":[2],"of":[3,40,92,96],"n":[4],"nonlinear":[5],"subsystems":[6,26],"in":[7,43,88],"the":[8,24,37,41,44,52,57,71,77,82,94],"input-to-state":[9],"stability":[10],"(ISS)":[11],"framework.":[12],"For":[13],"each":[14],"subsystem":[15],"an":[16],"ISS":[17,64],"Lyapunov":[18,65,79],"function":[19,66],"is":[20,33,67],"given":[21],"that":[22],"treats":[23],"other":[25],"as":[27,108],"independent":[28],"inputs.":[29],"A":[30],"gain":[31,49,58],"matrix":[32],"used":[34],"to":[35,103],"encode":[36],"mutual":[38],"dependencies":[39],"systems":[42],"network.":[45],"Under":[46],"a":[47,60,89],"small":[48],"assumption":[50],"on":[51],"monotone":[53],"operator":[54],"induced":[55],"by":[56,74],"matrix,":[59],"locally":[61],"Lipschitz":[62],"continuous":[63],"obtained":[68,87,107],"constructively":[69],"for":[70,81],"entire":[72],"network":[73],"appropriately":[75],"scaling":[76],"individual":[78],"functions":[80],"subsystems.":[83],"The":[84],"results":[85],"are":[86,106],"general":[90],"formulation":[91],"ISS;":[93],"cases":[95],"summation,":[97],"maximization,":[98],"and":[99],"separation":[100],"with":[101],"respect":[102],"external":[104],"gains":[105],"corollaries.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":12},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":25},{"year":2022,"cited_by_count":20},{"year":2021,"cited_by_count":25},{"year":2020,"cited_by_count":29},{"year":2019,"cited_by_count":25},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":22},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":19},{"year":2012,"cited_by_count":29}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2017-04-07T00:00:00"}