{"id":"https://openalex.org/W2133447038","doi":"https://doi.org/10.1109/cdc.2008.4739299","title":"Applications of the general Lyapunov ISS small-gain theorem for networks","display_name":"Applications of the general Lyapunov ISS small-gain theorem for networks","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2133447038","doi":"https://doi.org/10.1109/cdc.2008.4739299","mag":"2133447038"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4739299","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4739299","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":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004635071","display_name":"Sergey Dashkovskiy","orcid":"https://orcid.org/0000-0001-7049-012X"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sergey N. Dashkovskiy","raw_affiliation_strings":["Center of Applied Mathematics, University of Brethemen, Germany","Center of Appl. Math., Univ. of Bremen, Bremen, Germany"],"affiliations":[{"raw_affiliation_string":"Center of Applied Mathematics, University of Brethemen, Germany","institution_ids":[]},{"raw_affiliation_string":"Center of Appl. Math., Univ. of Bremen, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040557933","display_name":"Bj\u00f6rn S. R\u00fcffer","orcid":"https://orcid.org/0000-0001-8180-9773"},"institutions":[{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Bjorn S. Ruffer","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, University of Newcastle, Australia","Sch. of Electr. Eng., Univ. of Newcastle, Newcastle, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, University of Newcastle, Australia","institution_ids":["https://openalex.org/I78757542"]},{"raw_affiliation_string":"Sch. of Electr. Eng., Univ. of Newcastle, Newcastle, NSW, Australia","institution_ids":["https://openalex.org/I78757542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036100755","display_name":"Fabian Wirth","orcid":"https://orcid.org/0000-0002-2123-3714"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Fabian R. Wirth","raw_affiliation_strings":["Institute of Mathematics, University of W\u00fcrzburg, Germany","Inst. of Math., Univ. of Wurzburg, Wurzburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]},{"raw_affiliation_string":"Inst. of Math., Univ. of Wurzburg, Wurzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004635071"],"corresponding_institution_ids":["https://openalex.org/I180437899"],"apc_list":null,"apc_paid":null,"fwci":1.5248,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85572574,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"25","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998000264167786,"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":0.9998000264167786,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9991000294685364,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9988999962806702,"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/lyapunov-function","display_name":"Lyapunov function","score":0.8215736150741577},{"id":"https://openalex.org/keywords/small-gain-theorem","display_name":"Small-gain theorem","score":0.688992440700531},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.6643774509429932},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5833449959754944},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5341885089874268},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5305588245391846},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5265581607818604},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.4971754848957062},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4681309461593628},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45867568254470825},{"id":"https://openalex.org/keywords/resistor","display_name":"Resistor","score":0.44324102997779846},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.4313027560710907},{"id":"https://openalex.org/keywords/automatic-gain-control","display_name":"Automatic gain control","score":0.41876980662345886},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38096269965171814},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3725524842739105},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3590173125267029},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11857753992080688},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0971115231513977},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08870300650596619},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.06960436701774597}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.8215736150741577},{"id":"https://openalex.org/C27385263","wikidata":"https://www.wikidata.org/wiki/Q4165677","display_name":"Small-gain theorem","level":3,"score":0.688992440700531},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.6643774509429932},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5833449959754944},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5341885089874268},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5305588245391846},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5265581607818604},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.4971754848957062},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4681309461593628},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45867568254470825},{"id":"https://openalex.org/C137488568","wikidata":"https://www.wikidata.org/wiki/Q5321","display_name":"Resistor","level":3,"score":0.44324102997779846},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4313027560710907},{"id":"https://openalex.org/C177502760","wikidata":"https://www.wikidata.org/wiki/Q782524","display_name":"Automatic gain control","level":4,"score":0.41876980662345886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38096269965171814},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3725524842739105},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3590173125267029},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11857753992080688},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0971115231513977},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08870300650596619},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.06960436701774597},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"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":4,"locations":[{"id":"doi:10.1109/cdc.2008.4739299","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4739299","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.158.8695","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.8695","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.eng.unimelb.edu.au/brueffer/attachments/18.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/29033564","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Conference contribution"},{"id":"pmh:uon:6045","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.13/45157","pdf_url":null,"source":{"id":"https://openalex.org/S4306401391","display_name":"NOVA (University of Newcastle, Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78757542","host_organization_name":"University of Newcastle Australia","host_organization_lineage":["https://openalex.org/I78757542"],"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":"conference paper"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/29033564","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Conference contribution"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1548148540","https://openalex.org/W1960239420","https://openalex.org/W1978108057","https://openalex.org/W1994003949","https://openalex.org/W2003501930","https://openalex.org/W2006315891","https://openalex.org/W2012659334","https://openalex.org/W2014549417","https://openalex.org/W2017493230","https://openalex.org/W2027124517","https://openalex.org/W2028462202","https://openalex.org/W2036826525","https://openalex.org/W2045099285","https://openalex.org/W2098989671","https://openalex.org/W2134078068","https://openalex.org/W2139369541","https://openalex.org/W2144151364","https://openalex.org/W2145750077","https://openalex.org/W2761633506","https://openalex.org/W3106028347","https://openalex.org/W6644644706","https://openalex.org/W6651851813"],"related_works":["https://openalex.org/W2383986032","https://openalex.org/W2534107666","https://openalex.org/W2349796700","https://openalex.org/W3217133416","https://openalex.org/W3194517843","https://openalex.org/W2164487476","https://openalex.org/W2620928602","https://openalex.org/W2098989671","https://openalex.org/W4376456722","https://openalex.org/W1588802810"],"abstract_inverted_index":{"In":[0,27],"the":[1,4,18,32,39],"framework":[2],"of":[3,21,34,54,64],"ISS":[5,35,58],"Lyapunov":[6,22,36,59],"formulation":[7],"a":[8,68],"small":[9,42],"gain":[10,43],"theorem":[11],"has":[12],"recently":[13],"been":[14],"proved":[15],"which":[16],"allows":[17],"explicit":[19],"construction":[20],"functions":[23,37,60],"for":[24,61],"interconnected":[25],"systems.":[26],"this":[28],"note":[29],"we":[30],"recall":[31],"definitions":[33],"and":[38,55],"corresponding":[40],"general":[41],"theorems.":[44],"These":[45],"are":[46],"then":[47],"exemplarily":[48],"used":[49],"to":[50,56],"prove":[51],"input-to-state":[52],"stability":[53],"construct":[57],"four":[62],"areas":[63],"applications:":[65],"linear":[66],"systems,":[67],"Cohen-Grossberg":[69],"neuronal":[70],"network,":[71],"error":[72],"dynamics":[73],"in":[74],"formation":[75],"control,":[76],"as":[77,79],"well":[78],"nonlinear":[80],"transistor-linear":[81],"resistor":[82],"circuits.":[83]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
