{"id":"https://openalex.org/W2095605178","doi":"https://doi.org/10.1109/ecc.2015.7330560","title":"Determination of the optimal quadratic Lyapunov function for nonlinear autonomous systems via interval arithmetic","display_name":"Determination of the optimal quadratic Lyapunov function for nonlinear autonomous systems via interval arithmetic","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W2095605178","doi":"https://doi.org/10.1109/ecc.2015.7330560","mag":"2095605178"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2015.7330560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2015.7330560","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 European Control Conference (ECC)","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/A5015647756","display_name":"Robert Swiatlak","orcid":null},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Swiatlak","raw_affiliation_strings":["Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088168487","display_name":"Bernd Tibken","orcid":"https://orcid.org/0000-0002-4639-1487"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bernd Tibken","raw_affiliation_strings":["Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088684675","display_name":"Thomas Paradowski","orcid":null},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Paradowski","raw_affiliation_strings":["Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076349360","display_name":"Robert Dehnert","orcid":"https://orcid.org/0000-0002-0959-9035"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Dehnert","raw_affiliation_strings":["Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Faculty of Electrical, Information and Media Engineering University of Wuppertal D-42119, Germany","institution_ids":["https://openalex.org/I167360494"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I167360494"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"390","issue":null,"first_page":"297","last_page":"303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11236","display_name":"Control Systems and Identification","score":0.998199999332428,"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":0.9954000115394592,"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":0.7936359643936157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7099881768226624},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.6146528720855713},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.6136354804039001},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5714448094367981},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5520697236061096},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5203328132629395},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5093344449996948},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.50882488489151},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.5002729892730713},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.4664589464664459},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.44910547137260437},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.443342924118042},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43874645233154297},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3773423433303833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24013260006904602},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11950182914733887}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7936359643936157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7099881768226624},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.6146528720855713},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.6136354804039001},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5714448094367981},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5520697236061096},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5203328132629395},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5093344449996948},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.50882488489151},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.5002729892730713},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.4664589464664459},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.44910547137260437},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.443342924118042},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43874645233154297},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3773423433303833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24013260006904602},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11950182914733887},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"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/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","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":1,"locations":[{"id":"doi:10.1109/ecc.2015.7330560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2015.7330560","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W178772886","https://openalex.org/W1483384638","https://openalex.org/W1528301553","https://openalex.org/W1534906410","https://openalex.org/W1566391815","https://openalex.org/W1600295805","https://openalex.org/W1981734012","https://openalex.org/W2021313930","https://openalex.org/W2051138581","https://openalex.org/W2055255527","https://openalex.org/W2060602079","https://openalex.org/W2066745330","https://openalex.org/W2070381457","https://openalex.org/W2075265306","https://openalex.org/W2078592839","https://openalex.org/W2095715099","https://openalex.org/W2129492921","https://openalex.org/W2141662368","https://openalex.org/W2145072173","https://openalex.org/W2154341398","https://openalex.org/W2172200392","https://openalex.org/W2331214896","https://openalex.org/W4234844164","https://openalex.org/W4235812949"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W3217133416","https://openalex.org/W2358066536","https://openalex.org/W1970635650","https://openalex.org/W2496188264","https://openalex.org/W2126112326","https://openalex.org/W2091455539","https://openalex.org/W2333471870","https://openalex.org/W2374426356"],"abstract_inverted_index":{"The":[0,75],"estimation":[1,61,95,115],"of":[2,5,14,24,32,44,62,68,100,116],"the":[3,25,30,33,42,45,56,59,63,66,69,97,108,113,117,124],"Domain":[4],"Attraction":[6],"(DA)":[7],"is":[8],"an":[9,80,94],"important":[10],"topic":[11],"in":[12],"investigation":[13],"system":[15],"stability.":[16],"Using":[17],"Lyapunov's":[18],"conditions":[19],"leads":[20],"to":[21],"a":[22,38,52],"dependency":[23],"chosen":[26],"Lyapunov":[27,48,71],"function":[28,49,72],"and":[29],"size":[31,99],"estimation.":[34],"This":[35,111],"paper":[36],"presents":[37],"method,":[39],"which":[40,103],"delivers":[41,93],"coefficients":[43,67,76],"optimal":[46],"quadratic":[47,70],"(OQLF)":[50],"for":[51,96,123],"given":[53,125],"system.":[54,126],"Additionally":[55],"method":[57],"determines":[58],"largest":[60,114],"DA.":[64],"Therefore,":[65],"are":[73,77],"intervals.":[74,110],"optimized":[78],"by":[79],"iteratively":[81],"outer":[82],"optimization":[83,91],"algorithm":[84,92],"based":[85],"on":[86],"interval":[87],"arithmetic.":[88],"An":[89],"inner":[90],"DA's":[98],"all":[101],"QLF":[102],"can":[104],"be":[105],"constructed":[106],"from":[107],"coefficient":[109],"yields":[112],"DA":[118],"as":[119,121],"well":[120],"OQLF":[122]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
