{"id":"https://openalex.org/W2092334114","doi":"https://doi.org/10.1109/tac.2013.2289707","title":"Optimal Stabilization Using Lyapunov Measures","display_name":"Optimal Stabilization Using Lyapunov Measures","publication_year":2013,"publication_date":"2013-11-19","ids":{"openalex":"https://openalex.org/W2092334114","doi":"https://doi.org/10.1109/tac.2013.2289707","mag":"2092334114"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2289707","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2289707","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/A5038062267","display_name":"Arvind U. Raghunathan","orcid":"https://orcid.org/0000-0003-3173-3875"},"institutions":[{"id":"https://openalex.org/I4210159266","display_name":"Mitsubishi Electric (United States)","ror":"https://ror.org/053jnhe44","country_code":"US","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125","https://openalex.org/I4210159266"]},{"id":"https://openalex.org/I1306287861","display_name":"Mitsubishi Group (Japan)","ror":"https://ror.org/0234cd281","country_code":"JP","type":"company","lineage":["https://openalex.org/I1306287861"]}],"countries":["JP","US"],"is_corresponding":true,"raw_author_name":"Arvind Raghunathan","raw_affiliation_strings":["Mitsubishi Electric Research Laboratories, Cambridge, MA, United States of America","Mitsubishi Electr. Res. Laboratories, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Mitsubishi Electric Research Laboratories, Cambridge, MA, United States of America","institution_ids":["https://openalex.org/I4210159266"]},{"raw_affiliation_string":"Mitsubishi Electr. Res. Laboratories, Cambridge, MA, USA","institution_ids":["https://openalex.org/I1306287861"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050749492","display_name":"Umesh Vaidya","orcid":"https://orcid.org/0000-0002-0483-4921"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Umesh Vaidya","raw_affiliation_strings":["Department of Electrical & Computer Engineering, Iowa State University, Ames, IA, United States of America","Dept. of Electr. & Comput. Eng., Iowa State Univ., Ames, IA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, Iowa State University, Ames, IA, United States of America","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Iowa State Univ., Ames, IA, USA#TAB#","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038062267"],"corresponding_institution_ids":["https://openalex.org/I4210159266","https://openalex.org/I1306287861"],"apc_list":null,"apc_paid":null,"fwci":2.92994875,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.91772618,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"5","first_page":"1316","last_page":"1321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9972000122070312,"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/T11236","display_name":"Control Systems and Identification","score":0.9972000122070312,"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":0.9951000213623047,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9894999861717224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7892603278160095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6136338710784912},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5840121507644653},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5714422464370728},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5656258463859558},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.5097772479057312},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5006942749023438},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.49872732162475586},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4947333037853241},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.45124268531799316},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.44154107570648193},{"id":"https://openalex.org/keywords/transfer-operator","display_name":"Transfer operator","score":0.43036219477653503},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4195966124534607},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.41299015283584595},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.379020094871521},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3384743928909302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24678003787994385},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.16627654433250427},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1524403691291809},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1379190981388092}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7892603278160095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6136338710784912},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5840121507644653},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5714422464370728},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5656258463859558},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.5097772479057312},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5006942749023438},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.49872732162475586},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4947333037853241},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.45124268531799316},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.44154107570648193},{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.43036219477653503},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4195966124534607},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.41299015283584595},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.379020094871521},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3384743928909302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24678003787994385},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.16627654433250427},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1524403691291809},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1379190981388092},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2013.2289707","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2289707","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":[{"id":"https://openalex.org/F4320311090","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W122069695","https://openalex.org/W564963347","https://openalex.org/W1487586009","https://openalex.org/W1503092879","https://openalex.org/W1518039036","https://openalex.org/W1521510883","https://openalex.org/W1535396202","https://openalex.org/W1549382427","https://openalex.org/W1975228357","https://openalex.org/W1976237319","https://openalex.org/W1980496939","https://openalex.org/W1990337648","https://openalex.org/W1998433615","https://openalex.org/W2010654234","https://openalex.org/W2045938917","https://openalex.org/W2050383062","https://openalex.org/W2069876442","https://openalex.org/W2105260964","https://openalex.org/W2114599381","https://openalex.org/W2117450621","https://openalex.org/W2119697935","https://openalex.org/W2123871098","https://openalex.org/W2127273882","https://openalex.org/W2130415184","https://openalex.org/W2133330157","https://openalex.org/W2138025249","https://openalex.org/W2167916919","https://openalex.org/W2183870517","https://openalex.org/W2482944896","https://openalex.org/W3099133928","https://openalex.org/W4235178178","https://openalex.org/W4301014524","https://openalex.org/W6679511538"],"related_works":["https://openalex.org/W2383986032","https://openalex.org/W2349796700","https://openalex.org/W2534107666","https://openalex.org/W1970635650","https://openalex.org/W2496188264","https://openalex.org/W2979241488","https://openalex.org/W3194517843","https://openalex.org/W2118944249","https://openalex.org/W1517999927","https://openalex.org/W2588600327"],"abstract_inverted_index":{"Numerical":[0],"solutions":[1],"for":[2,39,79],"the":[3,13,27,51,68,73,80,88],"optimal":[4,40,52,89],"feedback":[5,84,91],"stabilization":[6,35,53,110],"of":[7,15,21,72,82,99,111],"discrete":[8],"time":[9],"dynamical":[10],"systems":[11],"is":[12,37,47,107],"focus":[14],"this":[16],"technical":[17],"note.":[18],"Set-theoretic":[19],"notion":[20],"almost":[22],"everywhere":[23],"stability":[24],"introduced":[25],"by":[26],"Lyapunov":[28,33],"measure,":[29],"weaker":[30],"than":[31],"conventional":[32],"function-based":[34],"methods,":[36],"used":[38,48,65],"stabilization.":[41],"The":[42,105],"linear":[43,59,74,103],"Perron-Frobenius":[44],"transfer":[45],"operator":[46],"to":[49,66],"pose":[50],"problem":[54],"as":[55,96],"an":[56],"infinite":[57],"dimensional":[58,70,102],"program.":[60,75,104],"Set-oriented":[61],"numerical":[62],"methods":[63],"are":[64],"obtain":[67],"finite":[69,101],"approximation":[71],"We":[76],"provide":[77],"conditions":[78],"existence":[81],"stabilizing":[83,90],"controls":[85],"and":[86],"show":[87],"control":[92],"can":[93],"be":[94],"obtained":[95],"a":[97,100,116],"solution":[98],"approach":[106],"demonstrated":[108],"on":[109],"period":[112],"two":[113],"orbit":[114],"in":[115],"controlled":[117],"standard":[118],"map.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}