{"id":"https://openalex.org/W2136861748","doi":"https://doi.org/10.1109/cdc.2007.4434742","title":"On interconnections of discontinuous dynamical systems: an input-to-state stability approach","display_name":"On interconnections of discontinuous dynamical systems: an input-to-state stability approach","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2136861748","doi":"https://doi.org/10.1109/cdc.2007.4434742","mag":"2136861748"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434742","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","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/A5063241688","display_name":"W.P.M.H. Heemels","orcid":"https://orcid.org/0000-0003-3440-8007"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"W.P.M.H. Heemels","raw_affiliation_strings":["Department of Mechanical Eng, Eindhovan University of Technology, Eindhoven, Netherlands","Embedded Systems Institute, Eindhoven, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Eng, Eindhovan University of Technology, Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Embedded Systems Institute, Eindhoven, Netherlands","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006584942","display_name":"S. Weiland","orcid":"https://orcid.org/0000-0002-6131-4658"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"S. Weiland","raw_affiliation_strings":["Department of Electrical Eng, Eindhovan University of Technology, Eindhoven, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Eng, Eindhovan University of Technology, Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":1.1443,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75709828,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"43","issue":null,"first_page":"109","last_page":"114"},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9968000054359436,"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":0.9940999746322632,"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":0.8110926747322083},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6024437546730042},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4902516007423401},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.47824135422706604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4619949162006378},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45971018075942993},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45044106245040894},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4481286108493805},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4408237338066101},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4140723645687103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38597074151039124},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17912185192108154},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1478840410709381},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13491320610046387},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11971655488014221},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0709587037563324},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06526210904121399}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.8110926747322083},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6024437546730042},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4902516007423401},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.47824135422706604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4619949162006378},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45971018075942993},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45044106245040894},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4481286108493805},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4408237338066101},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4140723645687103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38597074151039124},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17912185192108154},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1478840410709381},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13491320610046387},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11971655488014221},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0709587037563324},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06526210904121399},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/cdc.2007.4434742","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/ccbbbce3-0b8f-4f86-92d4-9f91025c6858","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/ccbbbce3-0b8f-4f86-92d4-9f91025c6858","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heemels, W P M H & Weiland, S 2007, On interconnections of discontinuous dynamical systems : an input-to-state stability approach. in Proceedings of the 46th Conference on Decision and Control (CDC 2007) 12-14 December 2007, New Orleans, Louisiana. Institute of Electrical and Electronics Engineers, Piscataway, pp. 109-114. https://doi.org/10.1109/CDC.2007.4434742","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:714106","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=714106","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:library.tue.nl:714106","is_oa":false,"landing_page_url":"http://repository.tue.nl/714106","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:oai-pmh.tno.nl:73943","is_oa":false,"landing_page_url":"https://resolver.tno.nl/uuid:fff17126-ee9e-429b-ac77-5c4d7f219049","pdf_url":null,"source":{"id":"https://openalex.org/S7407055233","display_name":"TNO Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/conferenceObject"},{"id":"pmh:tue:oai:pure.tue.nl:publications/ccbbbce3-0b8f-4f86-92d4-9f91025c6858","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/ccbbbce3-0b8f-4f86-92d4-9f91025c6858","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 46th Conference on Decision and Control (CDC 2007) 12-14 December 2007, New Orleans, Louisiana, 109 - 114","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W44162845","https://openalex.org/W1592648094","https://openalex.org/W1996505464","https://openalex.org/W2017493230","https://openalex.org/W2098989671","https://openalex.org/W2103277556","https://openalex.org/W2104958104","https://openalex.org/W2118741873","https://openalex.org/W2119655398","https://openalex.org/W2129492921","https://openalex.org/W2148993855","https://openalex.org/W2151136609","https://openalex.org/W2153570818","https://openalex.org/W2165626406","https://openalex.org/W2566720177","https://openalex.org/W4210718478","https://openalex.org/W6682653835"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W3194517843","https://openalex.org/W2534107666","https://openalex.org/W2374426356","https://openalex.org/W2121515234","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W1977987201","https://openalex.org/W2210722882"],"abstract_inverted_index":{"In":[0,82],"this":[1],"paper":[2,42],"we":[3],"will":[4],"extend":[5],"the":[6,28,35,47,69,108,117],"input-to-state":[7],"stability":[8,36],"(ISS)":[9],"framework":[10],"to":[11,60,131],"continuous-timediscontinuousdynamical":[12],"systems":[13,57,141],"(DDS)":[14],"adoptingnon-smoothISS":[15],"Lyapunov":[16,25,32,75,101,114,136],"functions.":[17],"The":[18],"main":[19],"motivation":[20],"for":[21,55,77,92,116,138],"investigating":[22],"non-smooth":[23,73,99],"ISS":[24,74,87,100,113,135],"functions":[26,137],"is":[27,53,66,90,105,120,123],"success":[29],"of":[30,38,46,63,71],"\"multiple":[31],"functions\"":[33],"in":[34,107],"analysis":[37],"hybrid":[39],"systems.":[40],"This":[41,103],"proposes":[43],"an":[44,111],"extension":[45],"well-known":[48],"Filippov":[49],"solution":[50],"concept,":[51],"that":[52,68,95,110],"appropriate":[54],"'open'":[56],"so":[58],"as":[59],"allow":[61],"interconnections":[62],"DDS.":[64],"It":[65,122],"proven":[67],"existence":[70],"a":[72,78,84,98],"function":[76,115],"DDS":[79,94],"implies":[80],"ISS.":[81],"addition,":[83],"(small":[85],"gain)":[86],"interconnection":[88],"theorem":[89],"derived":[91],"two":[93],"both":[96],"admit":[97],"function.":[102],"result":[104],"constructive":[106],"sense":[109],"explicit":[112],"interconnected":[118],"system":[119],"given.":[121],"shown":[124],"how":[125],"these":[126],"results":[127],"can":[128],"be":[129],"applied":[130],"construct":[132],"piecewise":[133,139],"quadratic":[134],"linear":[140,146],"(including":[142],"sliding":[143],"motions)":[144],"via":[145],"matrix":[147],"inequalities.":[148]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}