{"id":"https://openalex.org/W4231598087","doi":"https://doi.org/10.1109/cdc.2005.1583020","title":"Convergent piecewise affine systems: analysis and design Part II: discontinuous case","display_name":"Convergent piecewise affine systems: analysis and design Part II: discontinuous case","publication_year":2006,"publication_date":"2006-10-04","ids":{"openalex":"https://openalex.org/W4231598087","doi":"https://doi.org/10.1109/cdc.2005.1583020"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2005.1583020","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583020","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th 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/A5009007685","display_name":"Alexey Pavlov","orcid":"https://orcid.org/0000-0002-6211-6258"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"A. Pavlov","raw_affiliation_strings":["Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067237042","display_name":"A. Pogromsky","orcid":"https://orcid.org/0000-0001-8755-9832"},"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":"A. Pogromsky","raw_affiliation_strings":["Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004028181","display_name":"Nathan van de Wouw","orcid":"https://orcid.org/0000-0002-6745-9137"},"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":"N. van de Wouw","raw_affiliation_strings":["Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022300438","display_name":"Henk Nijmeijer","orcid":"https://orcid.org/0000-0001-5883-6191"},"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":"H. Nijmeijer","raw_affiliation_strings":["Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058620446","display_name":"Koos Rooda","orcid":null},"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":"K. Rooda","raw_affiliation_strings":["Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Eindhovan University of Technology, Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.236,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.88415362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"7","issue":null,"first_page":"5397","last_page":"5402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9998999834060669,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9998999834060669,"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":0.9926999807357788,"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":0.9925000071525574,"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/piecewise","display_name":"Piecewise","score":0.6993213891983032},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6972486972808838},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.692764401435852},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6452661752700806},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.627913773059845},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5953648090362549},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48005613684654236},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4629882574081421},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3303431272506714},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3094794452190399},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23919087648391724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23534464836120605},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11173942685127258},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08749234676361084},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08652576804161072},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07846757769584656}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6993213891983032},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6972486972808838},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.692764401435852},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6452661752700806},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.627913773059845},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5953648090362549},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48005613684654236},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4629882574081421},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3303431272506714},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3094794452190399},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23919087648391724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23534464836120605},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11173942685127258},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08749234676361084},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08652576804161072},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07846757769584656},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/cdc.2005.1583020","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583020","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/bb864aec-0970-474f-989a-504e839f3bc4","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/bb864aec-0970-474f-989a-504e839f3bc4","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":"Pavlov, A V, Pogromski, A Y, Wouw, van de, N, Nijmeijer, H & Rooda, J E 2005, Convergent piecewise affine systems : analysis and design Part II: discontinuous case. in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference(CDC-ECC), 12-15- december 2005, Seville, Spain. pp. on-CDROM. https://doi.org/10.1109/CDC.2005.1583020","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:661184","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=661184","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:661184","is_oa":false,"landing_page_url":"http://repository.tue.nl/661184","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:tue:oai:pure.tue.nl:publications/bb864aec-0970-474f-989a-504e839f3bc4","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/bb864aec-0970-474f-989a-504e839f3bc4","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 44th IEEE Conference on Decision and Control and European Control Conference(CDC-ECC), 12-15- december 2005, Seville, Spain, on - CDROM","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":14,"referenced_works":["https://openalex.org/W44162845","https://openalex.org/W1489723066","https://openalex.org/W1585294322","https://openalex.org/W2004802757","https://openalex.org/W2008663032","https://openalex.org/W2113593360","https://openalex.org/W2129492921","https://openalex.org/W2149266956","https://openalex.org/W2162484124","https://openalex.org/W2562854303","https://openalex.org/W3210839039","https://openalex.org/W4231598087","https://openalex.org/W4293244302","https://openalex.org/W6629226361"],"related_works":["https://openalex.org/W2385263368","https://openalex.org/W2038416447","https://openalex.org/W2364151838","https://openalex.org/W2347422947","https://openalex.org/W2061292372","https://openalex.org/W2353392568","https://openalex.org/W2377341410","https://openalex.org/W2066926363","https://openalex.org/W2142014702","https://openalex.org/W3009543351"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"convergence":[3,49],"properties":[4],"of":[5,25],"piecewise":[6],"affine":[7],"(PWA)":[8],"systems":[9,23,40],"with":[10,50],"discontinuous":[11,21,37],"right-hand":[12],"sides":[13],"are":[14,55],"studied.":[15],"It":[16],"is":[17,31],"shown":[18],"that":[19],"for":[20,34,45],"PWA":[22,39],"existence":[24],"a":[26,51],"common":[27],"quadratic":[28,46,52],"Lyapunov":[29,53],"function":[30],"not":[32],"sufficient":[33,43],"convergence.":[35],"For":[36],"bimodal":[38],"necessary":[41],"and":[42],"conditions":[44],"convergence,":[47],"i.e.":[48],"function,":[54],"derived.":[56]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
