{"id":"https://openalex.org/W2594978121","doi":"https://doi.org/10.1109/tac.2017.2682032","title":"A Note on Recursive Schur Complements, Block Hurwitz Stability of Metzler Matrices, and Related Results","display_name":"A Note on Recursive Schur Complements, Block Hurwitz Stability of Metzler Matrices, and Related Results","publication_year":2017,"publication_date":"2017-03-15","ids":{"openalex":"https://openalex.org/W2594978121","doi":"https://doi.org/10.1109/tac.2017.2682032","mag":"2594978121"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2682032","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2682032","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/A5008801364","display_name":"Matheus Souza","orcid":"https://orcid.org/0000-0002-1538-3361"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Matheus Souza","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036100755","display_name":"Fabian Wirth","orcid":"https://orcid.org/0000-0002-2123-3714"},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Fabian R. Wirth","raw_affiliation_strings":["Faculty of Computer Science and Mathematics, University of Passau, Passau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Mathematics, University of Passau, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036373073","display_name":"Robert Shorten","orcid":"https://orcid.org/0000-0002-9239-2499"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Robert N. Shorten","raw_affiliation_strings":["School of Electric, Electronic and Communications Engineering, University College Dublin, Dublin, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electric, Electronic and Communications Engineering, University College Dublin, Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1457,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.79426889,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"62","issue":"8","first_page":"4167","last_page":"4172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9930999875068665,"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/block","display_name":"Block (permutation group theory)","score":0.6541483402252197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5199188590049744},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5045715570449829},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39839959144592285},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3025192618370056},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3008546829223633},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22707390785217285}],"concepts":[{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6541483402252197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5199188590049744},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5045715570449829},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39839959144592285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3025192618370056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3008546829223633},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22707390785217285},{"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/tac.2017.2682032","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2682032","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":[{"id":"https://openalex.org/G7504877568","display_name":null,"funder_award_id":"11/PI/1177","funder_id":"https://openalex.org/F4320320847","funder_display_name":"Science Foundation Ireland"}],"funders":[{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W318380370","https://openalex.org/W613462629","https://openalex.org/W1488435683","https://openalex.org/W1970321745","https://openalex.org/W1981335650","https://openalex.org/W1996864164","https://openalex.org/W2008782864","https://openalex.org/W2018403127","https://openalex.org/W2054307315","https://openalex.org/W2061731692","https://openalex.org/W2062361291","https://openalex.org/W2063732874","https://openalex.org/W2065043066","https://openalex.org/W2068155564","https://openalex.org/W2073540225","https://openalex.org/W2085728653","https://openalex.org/W2092567339","https://openalex.org/W2094688944","https://openalex.org/W2111472560","https://openalex.org/W2130813144","https://openalex.org/W2144098960","https://openalex.org/W2145067072","https://openalex.org/W2156894914","https://openalex.org/W2344594675","https://openalex.org/W2962855705","https://openalex.org/W3210839039","https://openalex.org/W4233178228","https://openalex.org/W4235143360","https://openalex.org/W4241615413","https://openalex.org/W4295016751"],"related_works":["https://openalex.org/W3106133691","https://openalex.org/W4249580765","https://openalex.org/W2096753949","https://openalex.org/W2013082111","https://openalex.org/W2325858130","https://openalex.org/W1985218657","https://openalex.org/W1557945163","https://openalex.org/W2963341196","https://openalex.org/W2023661790","https://openalex.org/W2002593867"],"abstract_inverted_index":{"It":[0],"is":[1,33],"known":[2],"that":[3,36],"the":[4],"stability":[5,39],"of":[6,22,44,61,78],"a":[7,14,19],"Metzler":[8],"matrix":[9],"can":[10,48],"be":[11,49],"characterized":[12],"in":[13,29],"Routh-Hurwitz-like":[15],"fashion":[16],"based":[17],"on":[18],"recursive":[20],"application":[21],"scalar":[23],"Schur":[24],"complements":[25],"[1].":[26],"Our":[27],"objective":[28],"this":[30,45,62,79],"brief":[31],"note":[32],"to":[34,72],"show":[35],"recently":[37],"obtained":[38],"conditions":[40],"are":[41,64,70],"equivalent":[42],"statements":[43],"result":[46],"and":[47,67],"deduced":[50],"directly":[51],"therefrom":[52],"using":[53],"only":[54],"elementary":[55],"results":[56],"from":[57],"linear":[58],"algebra.":[59],"Implications":[60],"equivalence":[63],"also":[65],"discussed":[66],"several":[68],"examples":[69],"given":[71],"illustrate":[73],"potentially":[74],"interesting":[75],"system-theoretic":[76],"applications":[77],"observation.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}