{"id":"https://openalex.org/W3141509907","doi":"https://doi.org/10.1109/cdc.2011.6160302","title":"Approximate zero polynomials of polynomial matrices and linear systems","display_name":"Approximate zero polynomials of polynomial matrices and linear systems","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W3141509907","doi":"https://doi.org/10.1109/cdc.2011.6160302","mag":"3141509907"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160302","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","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/A5109080806","display_name":"Nicos Karcanias","orcid":null},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Nicos Karcanias","raw_affiliation_strings":["Systems and Control Research Centre, School of Engineering and Mathematical Sciences, City University, London, UK"],"affiliations":[{"raw_affiliation_string":"Systems and Control Research Centre, School of Engineering and Mathematical Sciences, City University, London, UK","institution_ids":["https://openalex.org/I180825142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004895976","display_name":"George Halikias","orcid":"https://orcid.org/0000-0003-1260-1383"},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"George Halikias","raw_affiliation_strings":["Systems and Control Research Centre, School of Engineering and Mathematical Sciences, City University, London, UK"],"affiliations":[{"raw_affiliation_string":"Systems and Control Research Centre, School of Engineering and Mathematical Sciences, City University, London, UK","institution_ids":["https://openalex.org/I180825142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109080806"],"corresponding_institution_ids":["https://openalex.org/I180825142"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.66049088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"241 243","issue":null,"first_page":"465","last_page":"470"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9991999864578247,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9902999997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.8604099154472351},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.7501100301742554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6799358129501343},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5808805823326111},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.5714308023452759},{"id":"https://openalex.org/keywords/reciprocal-polynomial","display_name":"Reciprocal polynomial","score":0.5138974189758301},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"Characteristic polynomial","score":0.448625385761261},{"id":"https://openalex.org/keywords/square-free-polynomial","display_name":"Square-free polynomial","score":0.4437553286552429},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.4229607880115509},{"id":"https://openalex.org/keywords/minimal-polynomial","display_name":"Minimal polynomial (linear algebra)","score":0.422598659992218},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3743126094341278},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3334905207157135},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22064536809921265},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12268111109733582}],"concepts":[{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.8604099154472351},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.7501100301742554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6799358129501343},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5808805823326111},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.5714308023452759},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.5138974189758301},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.448625385761261},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.4437553286552429},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.4229607880115509},{"id":"https://openalex.org/C30597210","wikidata":"https://www.wikidata.org/wiki/Q1163608","display_name":"Minimal polynomial (linear algebra)","level":5,"score":0.422598659992218},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3743126094341278},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3334905207157135},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22064536809921265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12268111109733582}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2011.6160302","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:openaccess.city.ac.uk:7297","is_oa":false,"landing_page_url":"https://openaccess.city.ac.uk/view/creators_id/n=2Ekarcanias.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401940","display_name":"City Research Online (City University London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I180825142","host_organization_name":"City, University of London","host_organization_lineage":["https://openalex.org/I180825142"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"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/W2001012051","https://openalex.org/W2014883276","https://openalex.org/W2018530368","https://openalex.org/W2073151503","https://openalex.org/W2074156531","https://openalex.org/W2080892223","https://openalex.org/W2084036924","https://openalex.org/W2085849252","https://openalex.org/W2086742230","https://openalex.org/W2140279008","https://openalex.org/W2142335183","https://openalex.org/W4388297455"],"related_works":["https://openalex.org/W2391577669","https://openalex.org/W1576380577","https://openalex.org/W4249593543","https://openalex.org/W2379712779","https://openalex.org/W1543706171","https://openalex.org/W2561847121","https://openalex.org/W2040308058","https://openalex.org/W1984423026","https://openalex.org/W2140446896","https://openalex.org/W4232548954"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"the":[3,21,31,46,56,60,119,123,140,144],"notions":[4],"of":[5,12,24,27,36,51,64,92,100,109,115,125,135,143],"approximate":[6,9,22,93],"and":[7,30,54,95,103],"optimal":[8,111],"zero":[10],"polynomial":[11,14,37,52,66,86],"a":[13,25,42,65,74,78,89,104],"matrix":[15],"by":[16],"deploying":[17],"recent":[18],"results":[19,40],"on":[20],"GCD":[23],"set":[26],"polynomials":[28],"[1]":[29],"exterior":[32],"algebra":[33],"[4]":[34,99],"representation":[35],"matrices.":[38],"The":[39,68,81,113],"provide":[41,55],"new":[43,90],"definition":[44],"for":[45,58,85,121],"\u201capproximate\u201d,":[47],"or":[48],"\u201calmost\u201d":[49],"zeros":[50,94,97],"matrices":[53,87],"means":[57,120],"computing":[59],"distance":[61,75,124],"from":[62,131],"non-coprimeness":[63],"matrix.":[67],"computational":[69],"framework":[70,83],"is":[71],"expressed":[72],"as":[73,137,139],"problem":[76],"in":[77],"projective":[79],"space.":[80],"general":[82],"defined":[84],"provides":[88,118],"characterization":[91],"decoupling":[96,146],"[2],":[98],"linear":[101],"systems":[102],"process":[105],"leading":[106],"to":[107],"computation":[108],"their":[110],"versions.":[112],"use":[114],"restriction":[116],"pencils":[117],"defining":[122],"state":[126],"feedback":[127],"(output":[128],"injection)":[129],"orbits":[130],"uncontrollable":[132],"(unobservable)":[133],"families":[134],"systems,":[136],"well":[138],"invariant":[141],"versions":[142],"\u201capproximate":[145],"polynomials\u201d.":[147]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
