{"id":"https://openalex.org/W2119073716","doi":"https://doi.org/10.1109/tac.2010.2041981","title":"Structural Instability and Minimal Realizations","display_name":"Structural Instability and Minimal Realizations","publication_year":2010,"publication_date":"2010-02-11","ids":{"openalex":"https://openalex.org/W2119073716","doi":"https://doi.org/10.1109/tac.2010.2041981","mag":"2119073716"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2041981","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2041981","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/A5032201822","display_name":"L.H. Keel","orcid":null},"institutions":[{"id":"https://openalex.org/I75256744","display_name":"Tennessee State University","ror":"https://ror.org/01fpczx89","country_code":"US","type":"education","lineage":["https://openalex.org/I75256744"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"L. H. Keel","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Tennessee State University, Nashville, TN, USA","Dept. of Electr. & Comput. Eng., Tennessee State Univ., Nashville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Tennessee State University, Nashville, TN, USA","institution_ids":["https://openalex.org/I75256744"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Tennessee State Univ., Nashville, TN, USA","institution_ids":["https://openalex.org/I75256744"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041121124","display_name":"S.P. Bhattacharyya","orcid":"https://orcid.org/0000-0001-9207-3298"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shankar P. Bhattacharyya","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX, USA","Dept. of Electr. & Comput. Eng, Texas A&M Univ., College Station, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Texas A&M Univ., College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032201822"],"corresponding_institution_ids":["https://openalex.org/I75256744"],"apc_list":null,"apc_paid":null,"fwci":2.1678,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.8966977,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"55","issue":"4","first_page":"1014","last_page":"1017"},"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":0.988099992275238,"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":0.988099992275238,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9843000173568726,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9690999984741211,"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/realization","display_name":"Realization (probability)","score":0.7518388032913208},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7460025548934937},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.6107069849967957},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.5585273504257202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5392275452613831},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5297625660896301},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.5262379050254822},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4907442331314087},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47643738985061646},{"id":"https://openalex.org/keywords/minimal-realization","display_name":"Minimal realization","score":0.4744074046611786},{"id":"https://openalex.org/keywords/transfer-matrix","display_name":"Transfer matrix","score":0.4301466643810272},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41035032272338867},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3234502077102661},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2819918692111969},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.27303802967071533},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.22621604800224304},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21611958742141724},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18556839227676392},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11409902572631836}],"concepts":[{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.7518388032913208},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7460025548934937},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.6107069849967957},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.5585273504257202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5392275452613831},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5297625660896301},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.5262379050254822},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4907442331314087},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47643738985061646},{"id":"https://openalex.org/C205609532","wikidata":"https://www.wikidata.org/wiki/Q770324","display_name":"Minimal realization","level":3,"score":0.4744074046611786},{"id":"https://openalex.org/C122890649","wikidata":"https://www.wikidata.org/wiki/Q7834016","display_name":"Transfer matrix","level":2,"score":0.4301466643810272},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41035032272338867},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3234502077102661},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2819918692111969},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.27303802967071533},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.22621604800224304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21611958742141724},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18556839227676392},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11409902572631836},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"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/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2010.2041981","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2041981","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W83533993","https://openalex.org/W793924815","https://openalex.org/W1490746760","https://openalex.org/W1500134124","https://openalex.org/W1534096605","https://openalex.org/W1556970733","https://openalex.org/W1574669531","https://openalex.org/W2122404944","https://openalex.org/W2135622003","https://openalex.org/W2149180331","https://openalex.org/W2613784664","https://openalex.org/W2798813531","https://openalex.org/W4213231302"],"related_works":["https://openalex.org/W2116285012","https://openalex.org/W2076195588","https://openalex.org/W2064234232","https://openalex.org/W2172052050","https://openalex.org/W4290705296","https://openalex.org/W75826713","https://openalex.org/W2147153839","https://openalex.org/W2561514193","https://openalex.org/W2016442955","https://openalex.org/W2369767786"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3],"consider":[4],"the":[5,25,31,42,59,62,68,76,83],"structural":[6,49],"stability":[7],"of":[8,41,61,75,79],"an":[9],"unstable":[10],"plant,":[11],"feedback":[12,33],"stabilized":[13],"by":[14],"a":[15,38,54],"controller.":[16],"It":[17],"is":[18,65],"shown":[19],"that":[20],"infinitesimal":[21],"parameter":[22,70],"perturbations":[23],"in":[24,52,57],"plant":[26,85],"transfer":[27,86],"matrix":[28,87],"can":[29],"destabilize":[30],"stable":[32],"control":[34],"system":[35],"obtained":[36],"from":[37],"minimal":[39,55],"realization":[40,56],"\u00bfnominal":[43],"plant.\u00bf":[44],"The":[45],"remedy":[46],"for":[47],"such":[48],"instability":[50],"consists":[51],"using":[53],"which":[58,82],"dimension":[60],"\u00bfantistable":[63],"part\u00bf":[64],"maximized":[66],"over":[67],"uncertain":[69],"values.":[71],"This":[72],"requires":[73],"knowledge":[74],"\u00bfcorrect":[77],"class\u00bf":[78],"parametrizations":[80],"to":[81],"nominal":[84],"belongs.":[88]},"counts_by_year":[{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}