{"id":"https://openalex.org/W2075999172","doi":"https://doi.org/10.1137/040612270","title":"Linear Complementarity Systems: Zeno States","display_name":"Linear Complementarity Systems: Zeno States","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2075999172","doi":"https://doi.org/10.1137/040612270","mag":"2075999172"},"language":"en","primary_location":{"id":"doi:10.1137/040612270","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612270","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":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://mdsoar.org/bitstreams/8dfd2e9e-02e4-4511-b1ca-571ca69b1682/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013733463","display_name":"Jinglai Shen","orcid":"https://orcid.org/0000-0003-2172-4182"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jinglai Shen","raw_affiliation_strings":["Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002789695","display_name":"Jong\u2010Shi Pang","orcid":"https://orcid.org/0000-0002-2224-6787"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jong-Shi Pang","raw_affiliation_strings":["Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180","institution_ids":["https://openalex.org/I165799507"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013733463"],"corresponding_institution_ids":["https://openalex.org/I165799507"],"apc_list":null,"apc_paid":null,"fwci":17.4444,"has_fulltext":true,"cited_by_count":89,"citation_normalized_percentile":{"value":0.99138279,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"44","issue":"3","first_page":"1040","last_page":"1066"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9947999715805054,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9947999715805054,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.973800003528595,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/zenos-paradoxes","display_name":"Zeno's paradoxes","score":0.8517362475395203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7482479214668274},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.659414529800415},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.5483808517456055},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4964812397956848},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.45666271448135376},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4214904308319092},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.41281354427337646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3806195557117462},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.33808547258377075},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3009808659553528},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2573372721672058}],"concepts":[{"id":"https://openalex.org/C7707877","wikidata":"https://www.wikidata.org/wiki/Q33378","display_name":"Zeno's paradoxes","level":2,"score":0.8517362475395203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7482479214668274},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.659414529800415},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.5483808517456055},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4964812397956848},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.45666271448135376},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4214904308319092},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.41281354427337646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3806195557117462},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.33808547258377075},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3009808659553528},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2573372721672058},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/040612270","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612270","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:mdsoar.org:11603/35914","is_oa":true,"landing_page_url":"http://hdl.handle.net/11603/35914","pdf_url":"https://mdsoar.org/bitstreams/8dfd2e9e-02e4-4511-b1ca-571ca69b1682/download","source":{"id":"https://openalex.org/S4306402556","display_name":"Maryland Shared Open Access Repository (USMAI Consortium)","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":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.551.111","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.551.111","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umbc.edu/~shenj/research/sicon_61227.pdf","raw_type":"text"},{"id":"doi:10.13016/m2e8e0-lied","is_oa":true,"landing_page_url":"https://doi.org/10.13016/m2e8e0-lied","pdf_url":null,"source":{"id":"https://openalex.org/S4306402644","display_name":"Digital Repository at the University of Maryland (University of Maryland College Park)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:mdsoar.org:11603/35914","is_oa":true,"landing_page_url":"http://hdl.handle.net/11603/35914","pdf_url":"https://mdsoar.org/bitstreams/8dfd2e9e-02e4-4511-b1ca-571ca69b1682/download","source":{"id":"https://openalex.org/S4306402556","display_name":"Maryland Shared Open Access Repository (USMAI Consortium)","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":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5025190442","display_name":"FRG:    Focused Research Collaborative Proposal:   Differential Algebraic Inequalities and their Applications in Engineering","funder_award_id":"0353216","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6176889518","display_name":"Computational Topics in Variational Inequalities and Complementarity Problems","funder_award_id":"0098013","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2075999172.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W189878098","https://openalex.org/W1534096605","https://openalex.org/W1543439990","https://openalex.org/W1561445488","https://openalex.org/W1594130515","https://openalex.org/W1908176971","https://openalex.org/W1965623622","https://openalex.org/W1993647205","https://openalex.org/W2000151369","https://openalex.org/W2017184164","https://openalex.org/W2030533255","https://openalex.org/W2060749138","https://openalex.org/W2068864491","https://openalex.org/W2081880850","https://openalex.org/W2085897137","https://openalex.org/W2095477585","https://openalex.org/W2096217592","https://openalex.org/W2098982596","https://openalex.org/W2105355605","https://openalex.org/W2109646661","https://openalex.org/W2112906954","https://openalex.org/W2116410318","https://openalex.org/W2119348011","https://openalex.org/W2119382067","https://openalex.org/W2120666720","https://openalex.org/W2121551043","https://openalex.org/W2136632272","https://openalex.org/W2138947309","https://openalex.org/W2149675356","https://openalex.org/W2163862895","https://openalex.org/W2164759324","https://openalex.org/W2170479723","https://openalex.org/W2580940564","https://openalex.org/W2948315098","https://openalex.org/W4231359949","https://openalex.org/W4252959020"],"related_works":["https://openalex.org/W2276648117","https://openalex.org/W819098253","https://openalex.org/W1548220668","https://openalex.org/W2765841216","https://openalex.org/W1566966152","https://openalex.org/W621787436","https://openalex.org/W2078891263","https://openalex.org/W169948756","https://openalex.org/W2789314275","https://openalex.org/W180570900"],"abstract_inverted_index":{"A":[0],"linear":[1,13,22],"complementarity":[2,23],"system":[3,9],"(LCS)":[4],"is":[5,29,37,75],"a":[6,12,20,68,79,86,131,141],"hybrid":[7,162],"dynamical":[8],"defined":[10],"by":[11,155,188],"time-invariant":[14],"ordinary":[15],"differential":[16],"equation":[17],"coupled":[18],"with":[19,44],"finite-dimensional":[21],"problem":[24],"(LCP).":[25],"The":[26,70],"present":[27],"paper":[28,49],"the":[30,51,57,83,96,99,114,124,167,171,178],"first":[31],"of":[32,53,60,63,72,78,91,95,101,134,170,182],"several":[33],"papers":[34],"whose":[35],"goal":[36],"to":[38,82,130,144],"study":[39,74],"some":[40],"fundamental":[41],"issues":[42],"associated":[43],"an":[45,76,92,105,111,128],"LCS.":[46],"Specifically,":[47],"this":[48,102],"addresses":[50],"issue":[52,59],"Zeno":[54,119],"states":[55],"and":[56,104,136,157,173,185,191],"related":[58,149],"finite":[61],"number":[62],"mode":[64],"switches":[65],"in":[66,89],"such":[67,127],"system.":[69],"cornerstone":[71],"our":[73,164],"expansion":[77,103],"solution":[80],"trajectory":[81],"LCS":[84,112,129,172],"near":[85],"given":[87,142],"state":[88,143],"terms":[90],"observability":[93],"degree":[94],"state.":[97],"On":[98],"basis":[100],"inductive":[106],"argument,":[107],"we":[108],"establish":[109],"that":[110,180],"satisfying":[113],"P-property":[115],"has":[116],"no":[117],"strongly":[118],"states.":[120],"We":[121],"next":[122],"extend":[123],"analysis":[125,165],"for":[126,140,159,177],"broader":[132],"class":[133],"problems":[135],"provide":[137],"sufficient":[138],"conditions":[139],"be":[145],"weakly":[146],"non-Zeno.":[147],"While":[148],"mode-switch":[150],"results":[151,176],"have":[152],"been":[153],"proved":[154],"Brunovsky":[156],"Sussmann":[158],"more":[160],"general":[161],"systems,":[163],"exploits":[166],"special":[168],"structure":[169],"yields":[174],"new":[175],"latter":[179],"are":[181],"independent":[183],"interest":[184],"complement":[186],"those":[187],"these":[189],"two":[190],"other":[192],"authors.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
