{"id":"https://openalex.org/W2092567339","doi":"https://doi.org/10.1109/tac.2014.2320303","title":"Classical Results on the Stability of Linear Time-Invariant Systems, and the Schwarz Form","display_name":"Classical Results on the Stability of Linear Time-Invariant Systems, and the Schwarz Form","publication_year":2014,"publication_date":"2014-04-25","ids":{"openalex":"https://openalex.org/W2092567339","doi":"https://doi.org/10.1109/tac.2014.2320303","mag":"2092567339"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2014.2320303","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2320303","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/A5036373073","display_name":"Robert Shorten","orcid":"https://orcid.org/0000-0002-9239-2499"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I4210145784","display_name":"IBM Research - Ireland","ror":"https://ror.org/04jnxr720","country_code":"IE","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210145784"]}],"countries":["IE","US"],"is_corresponding":true,"raw_author_name":"Robert Shorten","raw_affiliation_strings":["IBM Research Ireland, Mulhuddert, Dublin, Ireland","IBM Research - Ireland,Dublin,Ireland"],"affiliations":[{"raw_affiliation_string":"IBM Research Ireland, Mulhuddert, Dublin, Ireland","institution_ids":["https://openalex.org/I4210145784"]},{"raw_affiliation_string":"IBM Research - Ireland,Dublin,Ireland","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064848925","display_name":"Kumpati S. Narendra","orcid":"https://orcid.org/0009-0003-4826-3053"},"institutions":[{"id":"https://openalex.org/I4210155419","display_name":"Center for Systems Biology","ror":"https://ror.org/05r3dyn47","country_code":"US","type":"facility","lineage":["https://openalex.org/I136199984","https://openalex.org/I4210087915","https://openalex.org/I4210155419","https://openalex.org/I48633490"]},{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kumpati S. Narendra","raw_affiliation_strings":["Center for Systems Science, Yale University, New Haven, USA","Center for Syst. Sci., Yale Univ., New Haven, CT, USA"],"affiliations":[{"raw_affiliation_string":"Center for Systems Science, Yale University, New Haven, USA","institution_ids":["https://openalex.org/I4210155419","https://openalex.org/I32971472"]},{"raw_affiliation_string":"Center for Syst. Sci., Yale Univ., New Haven, CT, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036373073"],"corresponding_institution_ids":["https://openalex.org/I1341412227","https://openalex.org/I4210145784"],"apc_list":null,"apc_paid":null,"fwci":1.4243,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82504929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"59","issue":"11","first_page":"3020","last_page":"3025"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9968000054359436,"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":0.9968000054359436,"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":0.9933000206947327,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9926999807357788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/routh\u2013hurwitz-stability-criterion","display_name":"Routh\u2013Hurwitz stability criterion","score":0.8023084998130798},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6760704517364502},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.671101450920105},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5903502702713013},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5875703692436218},{"id":"https://openalex.org/keywords/hurwitz-matrix","display_name":"Hurwitz matrix","score":0.4984779357910156},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4911312758922577},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4865971803665161},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48288607597351074},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4383181631565094},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4110580086708069},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29910439252853394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17972803115844727},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08070623874664307},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07765138149261475},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07474762201309204},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07271826267242432},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.07059219479560852},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06411215662956238}],"concepts":[{"id":"https://openalex.org/C1366977","wikidata":"https://www.wikidata.org/wiki/Q2621270","display_name":"Routh\u2013Hurwitz stability criterion","level":3,"score":0.8023084998130798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6760704517364502},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.671101450920105},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5903502702713013},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5875703692436218},{"id":"https://openalex.org/C198931094","wikidata":"https://www.wikidata.org/wiki/Q2610096","display_name":"Hurwitz matrix","level":3,"score":0.4984779357910156},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4911312758922577},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4865971803665161},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48288607597351074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4383181631565094},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4110580086708069},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29910439252853394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17972803115844727},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08070623874664307},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07765138149261475},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07474762201309204},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07271826267242432},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.07059219479560852},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06411215662956238},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2014.2320303","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2320303","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"},{"id":"https://openalex.org/G8620179220","display_name":null,"funder_award_id":"ECS-0824118","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W594073344","https://openalex.org/W1496875698","https://openalex.org/W1575783483","https://openalex.org/W1978943682","https://openalex.org/W2052517919","https://openalex.org/W2105188618","https://openalex.org/W2111472560","https://openalex.org/W2128377848","https://openalex.org/W2128978199","https://openalex.org/W2135295287","https://openalex.org/W2144098960","https://openalex.org/W2320967943","https://openalex.org/W2798994937","https://openalex.org/W3104794861"],"related_works":["https://openalex.org/W2520906213","https://openalex.org/W2508418100","https://openalex.org/W2887374520","https://openalex.org/W1971038577","https://openalex.org/W2022729423","https://openalex.org/W2048318081","https://openalex.org/W1979223951","https://openalex.org/W3104794861","https://openalex.org/W2525499244","https://openalex.org/W2092567339"],"abstract_inverted_index":{"The":[0],"paper":[1],"deals":[2],"with":[3],"the":[4,15],"classical":[5],"results":[6,29],"of":[7,17,37],"Routh":[8],"and":[9,12],"Hurwitz,":[10],"Biehler":[11],"Kharitonov,":[13],"concerning":[14],"stability":[16],"a":[18,33],"linear":[19],"time":[20],"invariant":[21],"differential":[22],"equation.":[23],"It":[24],"is":[25],"shown":[26],"that":[27],"these":[28],"follow":[30],"directly":[31],"from":[32],"Schwarz":[34],"matrix":[35],"representation":[36],"stable":[38],"systems.":[39]},"counts_by_year":[{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
