{"id":"https://openalex.org/W1979035228","doi":"https://doi.org/10.1109/tac.2010.2042765","title":"Equivalence of Three Quadratic Approximation Methods of Stability Boundaries of Nonlinear Dynamic Systems","display_name":"Equivalence of Three Quadratic Approximation Methods of Stability Boundaries of Nonlinear Dynamic Systems","publication_year":2010,"publication_date":"2010-02-16","ids":{"openalex":"https://openalex.org/W1979035228","doi":"https://doi.org/10.1109/tac.2010.2042765","mag":"1979035228"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2042765","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2042765","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","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/A5042323553","display_name":"Lei Chen","orcid":"https://orcid.org/0000-0002-4778-4688"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Chen","raw_affiliation_strings":["State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing, China","Dept. of Electr. Eng., Tsinghua Univ., Beijing, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Tsinghua Univ., Beijing, China#TAB#","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020886065","display_name":"Yong Min","orcid":"https://orcid.org/0000-0003-2831-8427"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Min","raw_affiliation_strings":["State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing, China","Dept. of Electr. Eng., Tsinghua Univ., Beijing, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Tsinghua Univ., Beijing, China#TAB#","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07853279,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"5","first_page":"1258","last_page":"1262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9909999966621399,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9909999966621399,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.983299970626831,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9682000279426575,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/quadratic-equation","display_name":"Quadratic equation","score":0.7900195121765137},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.7744863033294678},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7198125123977661},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6596411466598511},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6010345220565796},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5883992910385132},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.547060489654541},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41779494285583496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27469271421432495},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14139127731323242},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.0672752857208252},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06171804666519165}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7900195121765137},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7744863033294678},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7198125123977661},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6596411466598511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6010345220565796},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5883992910385132},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.547060489654541},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41779494285583496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27469271421432495},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14139127731323242},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0672752857208252},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06171804666519165},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2010.2042765","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2042765","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1521492382","https://openalex.org/W1560647884","https://openalex.org/W2020459171","https://openalex.org/W2025496813","https://openalex.org/W2081257826","https://openalex.org/W2085210236","https://openalex.org/W2114860932","https://openalex.org/W2118225264","https://openalex.org/W2135249506","https://openalex.org/W2142940601","https://openalex.org/W4206651839","https://openalex.org/W6676855540"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W2354191502","https://openalex.org/W1972225038","https://openalex.org/W3134658850","https://openalex.org/W2355938171","https://openalex.org/W2780079842","https://openalex.org/W2115091349"],"abstract_inverted_index":{"Approximation":[0],"of":[1,4,16,41,46,59],"stable":[2],"manifolds":[3],"unstable":[5],"equilibrium":[6],"points":[7],"is":[8,32,51,72],"a":[9],"key":[10],"problem":[11],"in":[12,27,53],"stability":[13],"region":[14],"estimation":[15],"nonlinear":[17],"dynamic":[18],"systems.":[19],"Different":[20],"quadratic":[21,48],"approximation":[22,49],"methods":[23,50],"have":[24],"been":[25],"proposed":[26],"past":[28],"literature.":[29],"Then":[30],"what":[31],"their":[33],"relationship":[34],"and":[35,64],"which":[36],"has":[37],"better":[38],"performance":[39],"are":[40,62],"concern.":[42],"The":[43],"mathematical":[44],"equivalence":[45],"three":[47],"proved":[52],"this":[54],"note.":[55],"Their":[56],"computation":[57,70],"burdens":[58],"numerical":[60],"implementation":[61],"compared,":[63],"the":[65,68],"one":[66],"with":[67],"least":[69],"time":[71],"recommended":[73],"for":[74],"application.":[75]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}