{"id":"https://openalex.org/W1582848836","doi":"https://doi.org/10.1109/cdc.2002.1184721","title":"Robust D-stability of sets of polynomials with affine coefficients","display_name":"Robust D-stability of sets of polynomials with affine coefficients","publication_year":2003,"publication_date":"2003-08-27","ids":{"openalex":"https://openalex.org/W1582848836","doi":"https://doi.org/10.1109/cdc.2002.1184721","mag":"1582848836"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2002.1184721","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","raw_type":"proceedings-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/A5015539568","display_name":"A. Martinez-Cortes","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139671","display_name":"CETYS Universidad","ror":"https://ror.org/04gvszq17","country_code":"MX","type":"education","lineage":["https://openalex.org/I4210139671"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"A. Martinez-Cortes","raw_affiliation_strings":["Luz y Fuerza del Centro, Mexicali, Mexico","Luz y Fuerza del Centro, Mexico"],"affiliations":[{"raw_affiliation_string":"Luz y Fuerza del Centro, Mexicali, Mexico","institution_ids":["https://openalex.org/I4210139671"]},{"raw_affiliation_string":"Luz y Fuerza del Centro, Mexico","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015539568"],"corresponding_institution_ids":["https://openalex.org/I4210139671"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07416268,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"1440","last_page":"1446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.977400004863739,"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/mathematics","display_name":"Mathematics","score":0.8282879590988159},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.699844479560852},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6956064701080322},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6187146902084351},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5220265984535217},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.5054731369018555},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46091654896736145},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43842849135398865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43688127398490906},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.4257444441318512},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.406390517950058},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.3530702292919159},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3190041184425354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2694714665412903},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.2659212350845337},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08872097730636597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08668729662895203}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8282879590988159},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.699844479560852},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6956064701080322},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6187146902084351},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5220265984535217},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.5054731369018555},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46091654896736145},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43842849135398865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43688127398490906},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.4257444441318512},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.406390517950058},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.3530702292919159},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3190041184425354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2694714665412903},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.2659212350845337},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08872097730636597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08668729662895203},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2002.1184721","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1575783483","https://openalex.org/W1972097281","https://openalex.org/W1994891911","https://openalex.org/W1996745299","https://openalex.org/W2006427903","https://openalex.org/W2084613713","https://openalex.org/W2117461673","https://openalex.org/W2147664758","https://openalex.org/W2154087886","https://openalex.org/W2561628467","https://openalex.org/W2753704026","https://openalex.org/W6628461790","https://openalex.org/W6731114924"],"related_works":["https://openalex.org/W2051848833","https://openalex.org/W1565422586","https://openalex.org/W2510621088","https://openalex.org/W4386549132","https://openalex.org/W2296250081","https://openalex.org/W1888546338","https://openalex.org/W2964243396","https://openalex.org/W4287162593","https://openalex.org/W2949838243","https://openalex.org/W2057462664"],"abstract_inverted_index":{"The":[0,63,84,105],"determination":[1],"of":[2,6,9,46,49,65,91,103,108,113,126,131,141,143,147],"whether":[3],"all":[4,44],"roots":[5,87],"a":[7,17,21,55,100,119,124],"set":[8,107,150],"polynomials":[10,134],"P":[11,50,109],"with":[12],"affine":[13,52],"coefficients":[14,45],"are":[15,51,123],"inside":[16],"D":[18,67,92,137],"region":[19],"is":[20,72,93,116,135,154],"fundamental":[22],"problem":[23,39],"for":[24,86],"control":[25],"engineers.":[26],"In":[27],"this":[28],"paper":[29],"we":[30],"give":[31],"easy":[32],"testable":[33],"sufficient":[34],"conditions":[35],"to":[36],"solve":[37],"the":[38,41,70,75,81,89,97,139,144,148],"under":[40],"assumption":[42],"that":[43,152],"each":[47,111,114],"element":[48],"functions":[53],"over":[54],"common":[56],"compact":[57],"and":[58,80],"convex":[59],"multidimensional":[60],"domain":[61,98],"K.":[62],"kind":[64,125],"admissible":[66],"regions":[68],"where":[69],"method":[71],"applicable":[73],"include":[74],"open":[76],"left":[77],"complex":[78],"plane":[79],"unit":[82],"circle.":[83],"searching":[85],"on":[88,110,118],"boundary":[90],"done":[94],"by":[95],"partitioning":[96],"in":[99],"finite":[101],"number":[102],"subintervals.":[104],"value":[106,149],"point":[112],"subinterval":[115],"encapsulated":[117],"rectangle":[120],"whose":[121],"vertices":[122],"Kharitonov":[127],"polynomials.":[128],"If":[129],"one":[130],"these":[132],"four":[133],"not":[136],"stable,":[138],"analysis":[140],"part":[142],"exposed":[145],"edges":[146],"(on":[151],"subinterval)":[153],"required.":[155]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}