{"id":"https://openalex.org/W3011199294","doi":"https://doi.org/10.1109/cdc40024.2019.9030067","title":"Stability Analysis Via Refinement Of Piece-wise Linear Lyapunov Functions","display_name":"Stability Analysis Via Refinement Of Piece-wise Linear Lyapunov Functions","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3011199294","doi":"https://doi.org/10.1109/cdc40024.2019.9030067","mag":"3011199294"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9030067","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030067","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","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/A5062697455","display_name":"Hasan A. Poonawala","orcid":"https://orcid.org/0000-0003-4201-4745"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hasan A. Poonawala","raw_affiliation_strings":["Department of Mechanical Engineering, University of Kentucky, Lexington, KY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Kentucky, Lexington, KY, USA","institution_ids":["https://openalex.org/I143302722"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062697455"],"corresponding_institution_ids":["https://openalex.org/I143302722"],"apc_list":null,"apc_paid":null,"fwci":0.6653,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71978031,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":null,"first_page":"1442","last_page":"1447"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9857000112533569,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9857000112533569,"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/T10653","display_name":"Robot Manipulation and Learning","score":0.9853000044822693,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.972100019454956,"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/lyapunov-function","display_name":"Lyapunov function","score":0.8234291076660156},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6440058350563049},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.524289071559906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5230311155319214},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4881642460823059},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4852199852466583},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.470415860414505},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4663616418838501},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4651748836040497},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4327073097229004},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4303070306777954},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.4117577373981476},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40521448850631714},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3910902142524719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38102006912231445},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3445799946784973},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09453126788139343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06688091158866882}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.8234291076660156},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6440058350563049},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.524289071559906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5230311155319214},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4881642460823059},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4852199852466583},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.470415860414505},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4663616418838501},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4651748836040497},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4327073097229004},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4303070306777954},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.4117577373981476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40521448850631714},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3910902142524719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38102006912231445},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3445799946784973},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09453126788139343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06688091158866882},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/cdc40024.2019.9030067","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030067","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.75,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1495650726","https://openalex.org/W1855336155","https://openalex.org/W2048723778","https://openalex.org/W2068617307","https://openalex.org/W2099212405","https://openalex.org/W2118741873","https://openalex.org/W2129492921","https://openalex.org/W2489612911","https://openalex.org/W2973036620","https://openalex.org/W6639104331"],"related_works":["https://openalex.org/W2383986032","https://openalex.org/W1975178315","https://openalex.org/W2534107666","https://openalex.org/W2118944249","https://openalex.org/W2897919269","https://openalex.org/W2349796700","https://openalex.org/W1666234369","https://openalex.org/W2013435949","https://openalex.org/W2164487476","https://openalex.org/W2054171707"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2,55],"algorithm":[3,49],"for":[4],"finding":[5],"piece-wise":[6,16],"linear":[7,17],"Lyapunov":[8,34,68],"functions":[9],"that":[10],"verify":[11],"the":[12,33,42,46,61,67],"asymptotic":[13],"stability":[14],"of":[15,27,63],"differential":[18],"inclusions.":[19],"Existing":[20],"methods":[21,39],"either":[22],"use":[23,37],"a":[24],"fixed":[25],"set":[26,62],"pieces":[28],"(a":[29],"partition)":[30],"to":[31,40],"define":[32],"function,":[35],"or":[36],"heuristic":[38],"split":[41],"pieces,":[43],"thereby":[44],"refining":[45,52],"partition.":[47],"Our":[48],"involves":[50],"iteratively":[51],"partitions":[53],"using":[54],"exact":[56],"criterion":[57],"which":[58,66],"strictly":[59],"reduces":[60],"points":[64],"over":[65],"function":[69],"is":[70],"non-decreasing.":[71]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
