{"id":"https://openalex.org/W4415309719","doi":"https://doi.org/10.48550/arxiv.2507.12718","title":"Estimation of Regions of Attraction for Nonlinear Systems via Coordinate-Transformed TS Models and Piecewise Quadratic Lyapunov Functions","display_name":"Estimation of Regions of Attraction for Nonlinear Systems via Coordinate-Transformed TS Models and Piecewise Quadratic Lyapunov Functions","publication_year":2025,"publication_date":"2025-07-17","ids":{"openalex":"https://openalex.org/W4415309719","doi":"https://doi.org/10.48550/arxiv.2507.12718"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.12718","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.12718","pdf_url":"https://arxiv.org/pdf/2507.12718","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.12718","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071131213","display_name":"Artun Sel","orcid":"https://orcid.org/0000-0002-3142-3650"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sel, Artun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120047471","display_name":"Mehmet Koruturk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koruturk, Mehmet","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022288387","display_name":"Erdi Sayar","orcid":"https://orcid.org/0000-0002-5944-7291"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sayar, Erdi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.8317999839782715,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.8317999839782715,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10876","display_name":"Fault Detection and Control Systems","score":0.7117000222206116,"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/T10244","display_name":"Chaos control and synchronization","score":0.6898000240325928,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.8030999898910522},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7412999868392944},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6233999729156494},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5866000056266785},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.513700008392334},{"id":"https://openalex.org/keywords/coordinate-system","display_name":"Coordinate system","score":0.4977000057697296},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4487999975681305},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4415999948978424},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.39820000529289246}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8030999898910522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7415000200271606},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7412999868392944},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6233999729156494},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5866000056266785},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.513700008392334},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5044000148773193},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.4977000057697296},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4487999975681305},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4415999948978424},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.39820000529289246},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.39500001072883606},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3537999987602234},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33739998936653137},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.33149999380111694},{"id":"https://openalex.org/C184175843","wikidata":"https://www.wikidata.org/wiki/Q7191425","display_name":"Piecewise linear manifold","level":3,"score":0.3253999948501587},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.2937999963760376},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.2538999915122986},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.12718","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.12718","pdf_url":"https://arxiv.org/pdf/2507.12718","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"doi:10.48550/arxiv.2507.12718","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.12718","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.12718","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.12718","pdf_url":"https://arxiv.org/pdf/2507.12718","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,40,57],"novel":[4],"approach":[5,42,74],"for":[6,13,97],"computing":[7],"enlarged":[8],"Region":[9],"of":[10,20,43,59,119],"Attractions":[11],"(ROA)":[12],"nonlinear":[14,78],"dynamical":[15],"systems":[16],"through":[17,154],"the":[18,30,52,73,76,117,124],"integration":[19],"multiple":[21,64],"coordinate":[22,60,91],"transformations":[23,61],"and":[24,101],"piecewise":[25,106,128],"quadratic":[26,107,129,135],"Lyapunov":[27,108,130],"functions":[28,131],"within":[29],"Takagi-Sugeno":[31],"(TS)":[32],"modeling":[33],"framework.":[34],"While":[35],"existing":[36,158],"methods":[37],"typically":[38],"follow":[39],"single-path":[41],"original":[44,77],"system":[45,65,79],"$\\rightarrow$":[46,49],"TS":[47,95],"model":[48],"ROA":[50,70,112,144],"computation,":[51],"proposed":[53],"methodology":[54,139],"systematically":[55],"applies":[56],"sequence":[58],"to":[62,87,133,148],"generate":[63],"representations,":[66,92],"each":[67,98],"yielding":[68],"distinct":[69],"estimations.":[71],"Specifically,":[72],"transforms":[75],"using":[80,105],"transformation":[81],"matrices":[82],"$T_1,":[83],"T_2,":[84],"\\ldots,":[85],"T_N$":[86],"obtain":[88],"$N$":[89],"different":[90],"constructs":[93],"corresponding":[94],"models":[96],"transformed":[99],"system,":[100],"computes":[102],"individual":[103],"ROAs":[104],"functions.":[109],"The":[110,137],"final":[111],"estimate":[113],"is":[114],"obtained":[115],"as":[116,152],"union":[118],"all":[120],"computed":[121],"regions,":[122],"leveraging":[123],"flexibility":[125],"inherent":[126],"in":[127,143],"compared":[132,147],"traditional":[134],"approaches.":[136],"enhanced":[138],"demonstrates":[140],"significant":[141],"improvements":[142],"size":[145],"estimation":[146],"conventional":[149],"single-transformation":[150],"techniques,":[151],"evidenced":[153],"comparative":[155],"analysis":[156],"with":[157],"TS-based":[159],"stability":[160],"methods.":[161]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-18T00:00:00"}
