{"id":"https://openalex.org/W3008259057","doi":"https://doi.org/10.1109/tac.2020.2976297","title":"Comparison Between Different Notions of Stability for Laurent Systems","display_name":"Comparison Between Different Notions of Stability for Laurent Systems","publication_year":2020,"publication_date":"2020-02-26","ids":{"openalex":"https://openalex.org/W3008259057","doi":"https://doi.org/10.1109/tac.2020.2976297","mag":"3008259057"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.2976297","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.2976297","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/A5010998900","display_name":"Chirayu D. Athalye","orcid":"https://orcid.org/0000-0002-1147-2586"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Chirayu D. Athalye","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Science Bangalore, Bengaluru, India","Department of Electrical Engineering , Indian Institute of Science Bangalore, Bengaluru, India"],"raw_orcid":"https://orcid.org/0000-0002-1147-2586","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Science Bangalore, Bengaluru, India","institution_ids":["https://openalex.org/I59270414"]},{"raw_affiliation_string":"Department of Electrical Engineering , Indian Institute of Science Bangalore, Bengaluru, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022706065","display_name":"Debasattam Pal","orcid":"https://orcid.org/0000-0002-4886-3003"},"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":"Debasattam Pal","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","Dept. of Electrical Engineering, Indian Institute of Technology, Bombay, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0002-4886-3003","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Dept. of Electrical Engineering, Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","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, Mumbai, India","Dept. of Electrical Engineering, Indian Institute of Technology, Bombay, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0002-3934-9520","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Dept. of Electrical Engineering, Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010998900"],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":0.5951,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.65799337,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"66","issue":"2","first_page":"768","last_page":"772"},"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":0.9993000030517578,"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":0.9993000030517578,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/stability","display_name":"Stability (learning theory)","score":0.44608959555625916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28104454278945923},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.11118611693382263}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44608959555625916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28104454278945923},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.11118611693382263}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2020.2976297","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.2976297","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"},{"id":"pmh:oai:eprints.iisc.ac.in:68004","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401429","display_name":"ePrints@IISc (Indian Institute of Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5347857501","display_name":null,"funder_award_id":"IFA17-ENG227","funder_id":"https://openalex.org/F4320326272","funder_display_name":"Department of Science and Technology, Philippines"},{"id":"https://openalex.org/G7632939496","display_name":null,"funder_award_id":"IFA14-ENG99","funder_id":"https://openalex.org/F4320326272","funder_display_name":"Department of Science and Technology, Philippines"}],"funders":[{"id":"https://openalex.org/F4320326272","display_name":"Department of Science and Technology, Philippines","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W130632564","https://openalex.org/W1509036003","https://openalex.org/W1538686203","https://openalex.org/W1985703325","https://openalex.org/W2097415784","https://openalex.org/W2107221565","https://openalex.org/W2109197036","https://openalex.org/W2119052091","https://openalex.org/W2136598296","https://openalex.org/W2145949881","https://openalex.org/W2158124100","https://openalex.org/W2170883804","https://openalex.org/W2316003981","https://openalex.org/W2335062971","https://openalex.org/W2494897867","https://openalex.org/W2595897327","https://openalex.org/W2739817239","https://openalex.org/W2969308603","https://openalex.org/W3104949460","https://openalex.org/W3144501209","https://openalex.org/W6991908922"],"related_works":["https://openalex.org/W3036437122","https://openalex.org/W4311655097","https://openalex.org/W2362553105","https://openalex.org/W2238627405","https://openalex.org/W2340741275","https://openalex.org/W3159886541","https://openalex.org/W2611246911","https://openalex.org/W2890759410","https://openalex.org/W2749718331","https://openalex.org/W1539540014"],"abstract_inverted_index":{"In":[0],"this":[1,24,52],"article,":[2],"we":[3,125],"examine":[4],"a":[5,15,27],"particular":[6],"family":[7,25,53],"of":[8,54,81,92],"infinite-dimensional":[9],"discrete":[10],"autonomous":[11],"systems":[12,55],"given":[13],"by":[14],"first-order":[16],"state-space":[17],"equation;":[18],"the":[19,40,66,74,87,97,103,110,117,128],"state":[20],"transition":[21],"matrix":[22,30],"for":[23,65,94],"is":[26,39,134],"Laurent":[28,57,82,95],"polynomial":[29],"A(\u03c3,":[31],"\u03c3":[32,38],"<sup":[33,45,69,77,99,106,112,120,130],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[34,46,70,78,100,107,113,121,131],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[35],"),":[36],"where":[37],"shift":[41],"operator":[42],"on":[43],"R":[44],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[47],"-valued":[48],"sequences.":[49],"We":[50,59,84],"term":[51],"as":[56],"systems.":[58,83],"give":[60],"necessary":[61],"and":[62,73,116],"sufficient":[63],"conditions":[64],"exponential":[67,75,104,118],"\u2113":[68,76,98,105,111,119,129],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[71,101,108,132],"-stability":[72,80,133],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e</sup>":[79,114,122],"also":[85],"compare":[86],"following":[88],"four":[89],"different":[90],"notions":[91],"stability":[93],"systems:":[96],"-stability,":[102,109,115],"-stability;":[123],"furthermore,":[124],"conclude":[126],"that":[127],"an":[135],"outlier.":[136]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}