{"id":"https://openalex.org/W2125179080","doi":"https://doi.org/10.1109/tac.2010.2081710","title":"Robust Stability via Sign-Definite Decomposition","display_name":"Robust Stability via Sign-Definite Decomposition","publication_year":2010,"publication_date":"2010-09-29","ids":{"openalex":"https://openalex.org/W2125179080","doi":"https://doi.org/10.1109/tac.2010.2081710","mag":"2125179080"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2081710","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2081710","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, TN, 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, TN, 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":4.3356,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.94342113,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"1","first_page":"140","last_page":"145"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9954000115394592,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9943000078201294,"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/kharitonovs-theorem","display_name":"Kharitonov's theorem","score":0.8226238489151001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7551448345184326},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5794289708137512},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5662652254104614},{"id":"https://openalex.org/keywords/routh\u2013hurwitz-stability-criterion","display_name":"Routh\u2013Hurwitz stability criterion","score":0.5388095378875732},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5361314415931702},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45355090498924255},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.44778522849082947},{"id":"https://openalex.org/keywords/hurwitz-polynomial","display_name":"Hurwitz polynomial","score":0.43967029452323914},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43110978603363037},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.4248141646385193},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.42158347368240356},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.42140254378318787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3513615131378174},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.2735196352005005},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.2713908553123474},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.208425372838974},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14432236552238464},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13708996772766113},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12536311149597168}],"concepts":[{"id":"https://openalex.org/C173047080","wikidata":"https://www.wikidata.org/wiki/Q6400676","display_name":"Kharitonov's theorem","level":5,"score":0.8226238489151001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7551448345184326},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5794289708137512},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5662652254104614},{"id":"https://openalex.org/C1366977","wikidata":"https://www.wikidata.org/wiki/Q2621270","display_name":"Routh\u2013Hurwitz stability criterion","level":3,"score":0.5388095378875732},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5361314415931702},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45355090498924255},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.44778522849082947},{"id":"https://openalex.org/C120501884","wikidata":"https://www.wikidata.org/wiki/Q1414214","display_name":"Hurwitz polynomial","level":3,"score":0.43967029452323914},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43110978603363037},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.4248141646385193},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.42158347368240356},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.42140254378318787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3513615131378174},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2735196352005005},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2713908553123474},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.208425372838974},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14432236552238464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13708996772766113},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12536311149597168},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.0},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","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},{"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2010.2081710","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2081710","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W109843605","https://openalex.org/W1555808932","https://openalex.org/W1573672270","https://openalex.org/W1574669531","https://openalex.org/W1580755950","https://openalex.org/W1916017530","https://openalex.org/W2006692789","https://openalex.org/W2006890488","https://openalex.org/W2037102990","https://openalex.org/W2039277428","https://openalex.org/W2055027870","https://openalex.org/W2083212388","https://openalex.org/W2089258779","https://openalex.org/W2101314745","https://openalex.org/W2128838031","https://openalex.org/W2130101341","https://openalex.org/W2130515279","https://openalex.org/W2131946284","https://openalex.org/W2161706840","https://openalex.org/W2177779262","https://openalex.org/W2618328971","https://openalex.org/W3210839039","https://openalex.org/W4206956104","https://openalex.org/W6604518362"],"related_works":["https://openalex.org/W2054556934","https://openalex.org/W2128729640","https://openalex.org/W1975676515","https://openalex.org/W2015410487","https://openalex.org/W4253302468","https://openalex.org/W2143068244","https://openalex.org/W2990604479","https://openalex.org/W2090034561","https://openalex.org/W1486491956","https://openalex.org/W1951525531"],"abstract_inverted_index":{"This":[0,106],"paper":[1],"considers":[2],"the":[3,18,26,92,115,132,140,157],"problem":[4,23],"of":[5,8,17,20,28,54,60,91,94,110,117,143,153,159],"robust":[6],"stability":[7,79,90],"a":[9,29,41,48,52,77,85],"polynomial":[10,15],"family":[11,93,116,158],"whose":[12],"coefficients":[13,65],"are":[14,162],"functions":[16],"parameters":[19],"interests.":[21],"The":[22,57],"occurs":[24],"in":[25],"design":[27,43],"fixed":[30,33],"order":[31],"or":[32,128],"structure":[34],"multivariable":[35],"feedback":[36],"controller":[37],",":[38,46,50],"parametrized":[39],"by":[40],"real":[42],"parameter":[44],"vector":[45,53],"for":[47,88,139],"plant":[49],"containing":[51],"uncertain":[55,160],"parameters.":[56],"characteristic":[58],"polynomials":[59,118],"such":[61],"systems":[62,97],"often":[63],"contain":[64],"which":[66],"depend":[67],"polynomially":[68],"on":[69,74],"and":[70,101,150],".":[71],"Using":[72,146],"results":[73],"sign-definite":[75],"decomposition,":[76],"new":[78],"test":[80,107,133],"is":[81,108,121],"developed":[82],"that":[83,98,155],"gives":[84],"sufficient":[86],"condition":[87],"Hurwitz":[89],"closed":[95],"loop":[96],"result":[99],"when":[100],"vary":[102],"over":[103],"prescribed":[104],"boxes.":[105],"reminiscent":[109],"Kharitonov's":[111,137],"Theorem,":[112],"even":[113,129],"though":[114],"considered":[119],"here":[120],"certainly":[122],"not":[123],"restricted":[124],"to":[125,136],"be":[126],"interval":[127,144],"convex.":[130],"Moreover":[131],"does":[134],"reduce":[135],"Theorem":[138],"special":[141],"case":[142],"polynomials.":[145],"this":[147],"criterion":[148],"recursively":[149],"modularly,":[151],"sets":[152],"controllers":[154],"stabilize":[156],"plants":[161],"determined.":[163]},"counts_by_year":[{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
