{"id":"https://openalex.org/W2083862837","doi":"https://doi.org/10.1137/090749955","title":"Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions","display_name":"Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2083862837","doi":"https://doi.org/10.1137/090749955","mag":"2083862837"},"language":"en","primary_location":{"id":"doi:10.1137/090749955","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090749955","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"],"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/A5025056965","display_name":"Stefan Ratschan","orcid":"https://orcid.org/0000-0003-1710-1513"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Ratschan","raw_affiliation_strings":["stefan.ratschan@cs.cas.cz#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"stefan.ratschan@cs.cas.cz#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022816848","display_name":"Zhikun She","orcid":"https://orcid.org/0000-0003-2762-8730"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhikun She","raw_affiliation_strings":["zhikun.she@buaa.edu.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"zhikun.she@buaa.edu.cn#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7687,"has_fulltext":false,"cited_by_count":117,"citation_normalized_percentile":{"value":0.95178739,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"48","issue":"7","first_page":"4377","last_page":"4394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9962999820709229,"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/T10142","display_name":"Formal Methods in Verification","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8206124305725098},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.793351411819458},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.663500964641571},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6483078002929688},{"id":"https://openalex.org/keywords/attraction","display_name":"Attraction","score":0.5875980854034424},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4833647608757019},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4771708548069},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47587481141090393},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.445738285779953},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.43097859621047974},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3856884837150574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2581055164337158},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21112141013145447},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.20934149622917175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08410221338272095}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8206124305725098},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.793351411819458},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.663500964641571},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6483078002929688},{"id":"https://openalex.org/C2778364177","wikidata":"https://www.wikidata.org/wiki/Q2247133","display_name":"Attraction","level":2,"score":0.5875980854034424},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4833647608757019},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4771708548069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47587481141090393},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.445738285779953},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.43097859621047974},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3856884837150574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2581055164337158},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21112141013145447},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.20934149622917175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08410221338272095},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090749955","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090749955","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:asep.lib.cas.cz:CavUnEpca/0351298","is_oa":false,"landing_page_url":"http://hdl.handle.net/11104/0191083","pdf_url":null,"source":{"id":"https://openalex.org/S7407055266","display_name":"ASEP","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W10917309","https://openalex.org/W202123838","https://openalex.org/W1495927584","https://openalex.org/W1496537269","https://openalex.org/W1522228969","https://openalex.org/W1527177198","https://openalex.org/W1540125941","https://openalex.org/W1552875110","https://openalex.org/W1553142094","https://openalex.org/W1554063378","https://openalex.org/W1570787829","https://openalex.org/W1579164394","https://openalex.org/W1598317541","https://openalex.org/W1607353007","https://openalex.org/W1609596465","https://openalex.org/W1836569189","https://openalex.org/W1967845657","https://openalex.org/W1986264093","https://openalex.org/W1994738145","https://openalex.org/W2001579955","https://openalex.org/W2003141394","https://openalex.org/W2015041295","https://openalex.org/W2033891812","https://openalex.org/W2048801726","https://openalex.org/W2078414169","https://openalex.org/W2078899217","https://openalex.org/W2087749124","https://openalex.org/W2092007705","https://openalex.org/W2101993531","https://openalex.org/W2124856243","https://openalex.org/W2133520239","https://openalex.org/W2149179471","https://openalex.org/W2155330305","https://openalex.org/W2161142397","https://openalex.org/W2161491210","https://openalex.org/W2163182586","https://openalex.org/W2171505650","https://openalex.org/W2733990813"],"related_works":["https://openalex.org/W4386786398","https://openalex.org/W2138293586","https://openalex.org/W2080052720","https://openalex.org/W4319783074","https://openalex.org/W1503179180","https://openalex.org/W4319778501","https://openalex.org/W4255464147","https://openalex.org/W2021797003","https://openalex.org/W4313411469","https://openalex.org/W2949281083"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,34],"present":[4],"a":[5,9,14,29,56,79,96],"method":[6],"for":[7,17],"computing":[8],"basin":[10,23],"of":[11,24,51,58,92,98,104],"attraction":[12,25],"to":[13,55,75,95],"target":[15],"region":[16],"polynomial":[18,31],"ordinary":[19],"differential":[20],"equations.":[21],"This":[22,42],"is":[26],"ensured":[27],"by":[28,88],"Lyapunov-like":[30,53],"function":[32,54],"that":[33,62],"compute":[35],"using":[36],"an":[37,93],"interval":[38,60],"based":[39],"branch-and-relax":[40],"algorithm.":[41,90],"algorithm":[43],"relaxes":[44],"the":[45,49,52,89,102,105],"necessary":[46],"conditions":[47],"on":[48],"coefficients":[50],"system":[57],"linear":[59],"inequalities":[61],"can":[63],"then":[64],"be":[65,86],"solved":[66],"exactly.":[67],"It":[68],"iteratively":[69],"refines":[70],"these":[71],"relaxations":[72],"in":[73],"order":[74],"ensure":[76],"that,":[77],"whenever":[78],"nondegenerate":[80],"solution":[81],"exists,":[82],"it":[83],"will":[84],"eventually":[85],"found":[87],"Application":[91],"implementation":[94],"range":[97],"benchmark":[99],"problems":[100],"shows":[101],"usefulness":[103],"approach.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-21T08:15:58.654021","created_date":"2025-10-10T00:00:00"}