{"id":"https://openalex.org/W2065685935","doi":"https://doi.org/10.1109/icca.2014.6871096","title":"Complete characterization of the set of Lyapunov functions for the autonomous system &amp;#x1E8B;=&amp;#x2212;x","display_name":"Complete characterization of the set of Lyapunov functions for the autonomous system &amp;#x1E8B;=&amp;#x2212;x","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2065685935","doi":"https://doi.org/10.1109/icca.2014.6871096","mag":"2065685935"},"language":"en","primary_location":{"id":"doi:10.1109/icca.2014.6871096","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2014.6871096","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"11th IEEE International Conference on Control &amp; Automation (ICCA)","raw_type":"proceedings-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/A5010998900","display_name":"Chirayu D. Athalye","orcid":"https://orcid.org/0000-0002-1147-2586"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Chirayu D. Athalye","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology, Bombay, India","Dept. of Electr. Eng., Indian Inst. of Technol. Bombay, Mumbai, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology, Bombay, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Indian Inst. of Technol. Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013134999","display_name":"Harish K. Pillai","orcid":"https://orcid.org/0000-0002-3934-9520"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Harish K. Pillai","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology, Bombay, India","Dept. of Electr. Eng., Indian Inst. of Technol. Bombay, Mumbai, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology, Bombay, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Indian Inst. of Technol. Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022706065","display_name":"Debasattam Pal","orcid":"https://orcid.org/0000-0002-4886-3003"},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debasattam Pal","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology, Guwahati, India","Dept. of Electr. Eng., Indian Inst. of Technol., Guwahati, Guwahati, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology, Guwahati, India","institution_ids":["https://openalex.org/I1317621060"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Indian Inst. of Technol., Guwahati, Guwahati, India","institution_ids":["https://openalex.org/I1317621060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010998900"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14808044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":null,"first_page":"1221","last_page":"1225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9955000281333923,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9955000281333923,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9865999817848206,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8350768089294434},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7843219041824341},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.7380024790763855},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5351824164390564},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5198616981506348},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.491418719291687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4853190779685974},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45738285779953003},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.42058566212654114},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3814695477485657},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3812668025493622},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37369680404663086},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3417311906814575},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25614508986473083},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19695690274238586},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08358034491539001},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07649344205856323},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.07575035095214844},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06988051533699036},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.0600486695766449}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8350768089294434},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7843219041824341},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.7380024790763855},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5351824164390564},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5198616981506348},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.491418719291687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4853190779685974},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45738285779953003},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.42058566212654114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3814695477485657},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3812668025493622},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37369680404663086},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3417311906814575},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25614508986473083},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19695690274238586},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08358034491539001},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07649344205856323},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.07575035095214844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06988051533699036},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0600486695766449},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icca.2014.6871096","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2014.6871096","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"11th IEEE International Conference on Control &amp; Automation (ICCA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W94566284","https://openalex.org/W577564333","https://openalex.org/W2064551963","https://openalex.org/W2595897327","https://openalex.org/W4234534407","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W1996226968","https://openalex.org/W2284157877","https://openalex.org/W1789972284","https://openalex.org/W1986563546","https://openalex.org/W3039939495","https://openalex.org/W2314543451","https://openalex.org/W4229585693","https://openalex.org/W1586792688","https://openalex.org/W2776265842","https://openalex.org/W2780579194"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,103],"give":[4,104],"the":[5,14,32,71,76,99,116],"complete":[6],"characterization":[7,20],"of":[8,24,27,42,75,79,112],"all":[9],"possible":[10],"Lyapunov":[11,29,46,67],"functions":[12],"for":[13,120],"specific":[15],"autonomous":[16,100],"system":[17,43,101],"\u1e8b=-x.":[18],"This":[19],"is":[21,37,49,65,86],"in":[22,38,110],"terms":[23,111],"strict":[25,113],"quasi-convexity":[26,114],"a":[28,39,53,66,105],"candidate":[30],"at":[31,115],"equilibrium":[33,77,117],"point,":[34],"and":[35,82,91,107],"it":[36,48],"way":[40],"independent":[41],"dynamics.":[44],"From":[45],"theory":[47],"well":[50],"known":[51],"that,":[52],"continuously":[54],"differentiable":[55],"function":[56,68],"V":[57,85],":":[58],"\u211d":[59,64],"<sup":[60,93],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[61,94],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[62],"\u2192":[63],"to":[69,123],"conclude":[70],"global":[72],"asymptotic":[73],"stability":[74],"point":[78,118],"\u1e8b=-x":[80],"if":[81,84],"only":[83],"positive":[87],"definite,":[88],"radially":[89],"unbounded,":[90],"V\u0307(x)=-(\u2207V(x))":[92],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T</sup>":[95],"x<;0,":[96],"\u2200x\u22600.":[97],"For":[98],"\u1e8b=-x,":[102],"necessary":[106],"sufficient":[108],"condition,":[109],"0,":[119],"V\u0307":[121],"(\u00b7)":[122],"be":[124],"negative":[125],"definite.":[126]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}