{"id":"https://openalex.org/W2037963983","doi":"https://doi.org/10.1109/cdc.2013.6760403","title":"A characterization of solutions for general copositive quadratic Lyapunov inequalities","display_name":"A characterization of solutions for general copositive quadratic Lyapunov inequalities","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2037963983","doi":"https://doi.org/10.1109/cdc.2013.6760403","mag":"2037963983"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6760403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","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/A5102726557","display_name":"Kwang\u2010Ki K. Kim","orcid":"https://orcid.org/0000-0002-6324-3283"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kwang-Ki K. Kim","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083684552","display_name":"Richard D. Braatz","orcid":"https://orcid.org/0000-0003-4304-3484"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard D. Braatz","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA","Massachusetts Institute of Technology; ,; Cambridge MA USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology; ,; Cambridge MA USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.936,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68635038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"45","issue":null,"first_page":"3397","last_page":"3402"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9991999864578247,"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":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7143130898475647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7035982012748718},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.49397188425064087},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.49335089325904846},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48297157883644104},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.47718918323516846},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4318867325782776},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.41857296228408813},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4132035970687866},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3727257251739502},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.17674750089645386},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14015477895736694},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11257606744766235},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.100108802318573}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7143130898475647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7035982012748718},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.49397188425064087},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.49335089325904846},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48297157883644104},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.47718918323516846},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4318867325782776},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.41857296228408813},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4132035970687866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3727257251739502},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.17674750089645386},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14015477895736694},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11257606744766235},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.100108802318573},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2013.6760403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"},{"id":"https://openalex.org/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1488435683","https://openalex.org/W1500921805","https://openalex.org/W1534416612","https://openalex.org/W1632601927","https://openalex.org/W1976209547","https://openalex.org/W1985273793","https://openalex.org/W2005226933","https://openalex.org/W2017465297","https://openalex.org/W2019854158","https://openalex.org/W2028739770","https://openalex.org/W2073540225","https://openalex.org/W2079135578","https://openalex.org/W2114472256","https://openalex.org/W4235143360","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W1488834356","https://openalex.org/W1996715315","https://openalex.org/W2003652915","https://openalex.org/W2952786252","https://openalex.org/W4288333574","https://openalex.org/W3046115410"],"abstract_inverted_index":{"This":[0,60],"article":[1,61],"provides":[2,62],"answers":[3],"to":[4,13,135],"an":[5,87],"open":[6],"question":[7],"raised":[8],"in":[9,78,111],"[1]":[10],"with":[11],"regard":[12],"checking":[14],"existence":[15,48],"of":[16,42,49,73,86,95,129,140,143],"a":[17,31,44,50,63,108,112,117],"solution":[18,53],"for":[19,40,54,71,83,145],"general":[20],"copositive":[21,57,146],"Lyapunov":[22,52,58,147],"inequalities.":[23,148],"We":[24,123],"consider":[25],"homogeneous":[26],"LTI":[27,76],"systems":[28],"that":[29,125],"preserve":[30],"proper":[32,109],"cone":[33,110],"C.*":[34],"A":[35],"necessary":[36,67],"and":[37,68,97,115],"sufficient":[38,69],"condition":[39,70],"stability":[41,72,85],"such":[43],"system":[45],"is":[46,107],"the":[47,55,74,84,93,126,137,141],"quadratic":[51],"associated":[56],"inequality.":[59],"computationally":[64],"efficient":[65],"alternative":[66],"cone-invariant":[75],"system,":[77],"which":[79],"geometric":[80],"algebraic":[81],"conditions":[82,101,131],"equilibrium":[88],"state":[89],"are":[90,102],"established":[91],"from":[92],"concepts":[94],"dual":[96],"polar":[98],"cones.":[99],"The":[100],"polynomial-time":[103,118],"verifiable,":[104],"provided":[105],"C":[106],"Hilbert":[113],"space":[114],"has":[116],"evaluable":[119],"self-concordant":[120],"barrier":[121],"function.":[122],"show":[124],"feasible":[127],"solutions":[128,144],"those":[130],"can":[132],"be":[133],"used":[134],"characterize":[136],"extreme":[138],"rays":[139],"set":[142]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
