{"id":"https://openalex.org/W2021012570","doi":"https://doi.org/10.1109/tac.2013.2241472","title":"Optimization of Lyapunov Invariants in Verification of Software Systems","display_name":"Optimization of Lyapunov Invariants in Verification of Software Systems","publication_year":2013,"publication_date":"2013-01-21","ids":{"openalex":"https://openalex.org/W2021012570","doi":"https://doi.org/10.1109/tac.2013.2241472","mag":"2021012570"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2241472","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2241472","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/A5086502993","display_name":"Mardavij Roozbehani","orcid":null},"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"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. Roozbehani","raw_affiliation_strings":["Laboratory for Information and Decision Systems (LIDS), Department of Electrical Engineering and ComputerScience (EECS), Massachusetts Institute of Technology, Cambridge, MA, USA","[Dept. of Electr. Eng. & Comput. Sci. (EECS), Massachusetts Inst. of Technol., Cambridge, MA, USA]"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Department of Electrical Engineering and ComputerScience (EECS), Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Dept. of Electr. Eng. & Comput. Sci. (EECS), Massachusetts Inst. of Technol., Cambridge, MA, USA]","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108208983","display_name":"Alexandre Megretski","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"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":"A. Megretski","raw_affiliation_strings":["Laboratory for Information and Decision Systems (LIDS), Department of Electrical Engineering and ComputerScience (EECS), Massachusetts Institute of Technology, Cambridge, MA, USA","[Dept. of Electr. Eng. & Comput. Sci. (EECS), Massachusetts Inst. of Technol., Cambridge, MA, USA]"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Department of Electrical Engineering and ComputerScience (EECS), Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Dept. of Electr. Eng. & Comput. Sci. (EECS), Massachusetts Inst. of Technol., Cambridge, MA, USA]","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041459160","display_name":"\u00c9ric F\u00e9ron","orcid":"https://orcid.org/0000-0001-7717-2159"},"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":"E. Feron","raw_affiliation_strings":["School of AeroSpace Engineering, Georgia Institute of Technology, Atlanta, GA, USA","Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"School of AeroSpace Engineering, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086502993"],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":4.0684,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.93827512,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"58","issue":"3","first_page":"696","last_page":"711"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9995999932289124,"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/T10142","display_name":"Formal Methods in Verification","score":0.9995999932289124,"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/T10933","display_name":"Real-Time Systems Scheduling","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T12423","display_name":"Software Reliability and Analysis Research","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.7462838292121887},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.6067890524864197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5726457834243774},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5076745748519897},{"id":"https://openalex.org/keywords/software-verification","display_name":"Software verification","score":0.4931144416332245},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4927676022052765},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.46483656764030457},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4273070991039276},{"id":"https://openalex.org/keywords/software-system","display_name":"Software system","score":0.3047175407409668},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30283063650131226},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.25576549768447876},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.19460684061050415},{"id":"https://openalex.org/keywords/software-construction","display_name":"Software construction","score":0.19380974769592285},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1442922055721283}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7462838292121887},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.6067890524864197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5726457834243774},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5076745748519897},{"id":"https://openalex.org/C33054407","wikidata":"https://www.wikidata.org/wiki/Q6504747","display_name":"Software verification","level":5,"score":0.4931144416332245},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4927676022052765},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.46483656764030457},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4273070991039276},{"id":"https://openalex.org/C149091818","wikidata":"https://www.wikidata.org/wiki/Q2429814","display_name":"Software system","level":3,"score":0.3047175407409668},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30283063650131226},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.25576549768447876},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.19460684061050415},{"id":"https://openalex.org/C186846655","wikidata":"https://www.wikidata.org/wiki/Q3398377","display_name":"Software construction","level":4,"score":0.19380974769592285},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1442922055721283},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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.2013.2241472","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2241472","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":107,"referenced_works":["https://openalex.org/W89892127","https://openalex.org/W120333500","https://openalex.org/W431400460","https://openalex.org/W564144495","https://openalex.org/W1480909796","https://openalex.org/W1486448317","https://openalex.org/W1488202922","https://openalex.org/W1488872683","https://openalex.org/W1503887525","https://openalex.org/W1526045365","https://openalex.org/W1530375435","https://openalex.org/W1533503276","https://openalex.org/W1539457702","https://openalex.org/W1539838732","https://openalex.org/W1540180001","https://openalex.org/W1540897666","https://openalex.org/W1542648917","https://openalex.org/W1552843130","https://openalex.org/W1553894716","https://openalex.org/W1557311886","https://openalex.org/W1557561422","https://openalex.org/W1564078679","https://openalex.org/W1587475735","https://openalex.org/W1598634407","https://openalex.org/W1608230613","https://openalex.org/W1676597814","https://openalex.org/W1755257908","https://openalex.org/W1762430620","https://openalex.org/W1772454844","https://openalex.org/W1783633569","https://openalex.org/W1863722042","https://openalex.org/W1865218796","https://openalex.org/W1961645642","https://openalex.org/W1967073510","https://openalex.org/W1967091946","https://openalex.org/W1967184028","https://openalex.org/W1968143987","https://openalex.org/W1971837993","https://openalex.org/W1977985274","https://openalex.org/W1985123706","https://openalex.org/W1991612348","https://openalex.org/W1992008263","https://openalex.org/W1994475353","https://openalex.org/W2001033871","https://openalex.org/W2002089154","https://openalex.org/W2004463571","https://openalex.org/W2009288822","https://openalex.org/W2009965218","https://openalex.org/W2026018724","https://openalex.org/W2029402321","https://openalex.org/W2032173185","https://openalex.org/W2033118636","https://openalex.org/W2037708677","https://openalex.org/W2041152728","https://openalex.org/W2043100293","https://openalex.org/W2050383062","https://openalex.org/W2050707981","https://openalex.org/W2052970196","https://openalex.org/W2066666147","https://openalex.org/W2076535438","https://openalex.org/W2080267935","https://openalex.org/W2088017390","https://openalex.org/W2091316349","https://openalex.org/W2097944741","https://openalex.org/W2098022036","https://openalex.org/W2101508170","https://openalex.org/W2105614525","https://openalex.org/W2106264302","https://openalex.org/W2114614628","https://openalex.org/W2118741873","https://openalex.org/W2122914790","https://openalex.org/W2124909257","https://openalex.org/W2127520982","https://openalex.org/W2129492921","https://openalex.org/W2133404041","https://openalex.org/W2136333450","https://openalex.org/W2137777756","https://openalex.org/W2141881497","https://openalex.org/W2142283990","https://openalex.org/W2142785340","https://openalex.org/W2152185829","https://openalex.org/W2155689575","https://openalex.org/W2159756689","https://openalex.org/W2163629033","https://openalex.org/W2165281529","https://openalex.org/W2165748475","https://openalex.org/W2182510773","https://openalex.org/W2259853674","https://openalex.org/W2271183319","https://openalex.org/W2326644268","https://openalex.org/W2340735175","https://openalex.org/W2505968561","https://openalex.org/W2507913385","https://openalex.org/W2536620281","https://openalex.org/W2565969279","https://openalex.org/W2575702446","https://openalex.org/W2912522929","https://openalex.org/W2913459036","https://openalex.org/W2962725330","https://openalex.org/W3034208633","https://openalex.org/W3210839039","https://openalex.org/W4232668957","https://openalex.org/W4240548942","https://openalex.org/W4243620103","https://openalex.org/W4251032486","https://openalex.org/W4299546310","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W2383986032","https://openalex.org/W2534107666","https://openalex.org/W2118944249","https://openalex.org/W2897919269","https://openalex.org/W2349796700","https://openalex.org/W2164487476","https://openalex.org/W3217133416","https://openalex.org/W2775440879","https://openalex.org/W1977987201","https://openalex.org/W118344564"],"abstract_inverted_index":{"The":[0,26,106],"paper":[1],"proposes":[2],"a":[3,115,129],"control-theoretic":[4],"framework":[5,81],"for":[6,108,131],"verification":[7,16,46],"of":[8,21,47,62,65,72,90,100],"numerical":[9],"software":[10,15,49],"systems,":[11],"and":[12,23,33,42,51,74,94],"puts":[13],"forward":[14],"as":[17,114],"an":[18],"important":[19],"application":[20],"control":[22,39],"systems":[24,40],"theory.":[25],"idea":[27],"is":[28,124,128],"to":[29,45,60,79,98],"transfer":[30],"Lyapunov":[31,83,101],"functions":[32,89],"the":[34,91,103,109,120,126,132],"associated":[35,121],"computational":[36],"techniques":[37],"from":[38],"analysis":[41],"convex":[43,116],"optimization":[44,117,122],"various":[48],"safety":[50],"performance":[52],"specifications.":[53],"These":[54,85],"include":[55],"but":[56],"are":[57,82,86],"not":[58],"limited":[59],"absence":[61,64,71],"overflow,":[63],"division-by-zero,":[66],"termination":[67],"in":[68],"finite":[69],"time,":[70],"dead-code,":[73],"certain":[75,96],"user-specified":[76],"assertions.":[77],"Central":[78],"this":[80],"invariants.":[84],"properly":[87],"constructed":[88],"program":[92],"variables,":[93],"satisfy":[95],"properties\u2014analogous":[97],"those":[99],"functions\u2014along":[102],"execution":[104],"trace.":[105],"search":[107],"invariants":[110],"can":[111],"be":[112],"formulated":[113],"problem.":[118],"If":[119],"problem":[123],"feasible,":[125],"result":[127],"certificate":[130],"specification.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}