{"id":"https://openalex.org/W2728475743","doi":"https://doi.org/10.1109/access.2017.2722417","title":"Precise Characterizations of the Stability Margin in Time-Domain Space for Planar Systems Undergoing Periodic Switching","display_name":"Precise Characterizations of the Stability Margin in Time-Domain Space for Planar Systems Undergoing Periodic Switching","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2728475743","doi":"https://doi.org/10.1109/access.2017.2722417","mag":"2728475743"},"language":"en","primary_location":{"id":"doi:10.1109/access.2017.2722417","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2017.2722417","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2017.2722417","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081609833","display_name":"Zunbing Sheng","orcid":"https://orcid.org/0000-0001-7647-5326"},"institutions":[{"id":"https://openalex.org/I55022517","display_name":"Heilongjiang University","ror":"https://ror.org/04zyhq975","country_code":"CN","type":"education","lineage":["https://openalex.org/I55022517"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zunbing Sheng","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Heilongjiang University, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0001-7647-5326","affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Heilongjiang University, Harbin, China","institution_ids":["https://openalex.org/I55022517"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053946410","display_name":"Wei Qian","orcid":"https://orcid.org/0000-0002-3994-6501"},"institutions":[{"id":"https://openalex.org/I4210166499","display_name":"Henan Polytechnic University","ror":"https://ror.org/05vr1c885","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Qian","raw_affiliation_strings":["School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China","institution_ids":["https://openalex.org/I4210166499"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.1984,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.49771085,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":null,"first_page":"12224","last_page":"12229"},"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":0.9994000196456909,"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":0.9994000196456909,"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":0.9976999759674072,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9965999722480774,"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/exponential-stability","display_name":"Exponential stability","score":0.6797353625297546},{"id":"https://openalex.org/keywords/dwell-time","display_name":"Dwell time","score":0.6463603973388672},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6351996660232544},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6205991506576538},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6012876629829407},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5433902740478516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5373157262802124},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5136296153068542},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.46233057975769043},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44841212034225464},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43261483311653137},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.412391722202301},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3948201537132263},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3668619394302368},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3605138957500458},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.339296817779541},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15209272503852844},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12456250190734863},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10703009366989136},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10009780526161194},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07944920659065247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07855004072189331},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06758403778076172}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6797353625297546},{"id":"https://openalex.org/C151637689","wikidata":"https://www.wikidata.org/wiki/Q5318064","display_name":"Dwell time","level":2,"score":0.6463603973388672},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6351996660232544},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6205991506576538},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6012876629829407},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5433902740478516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5373157262802124},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5136296153068542},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.46233057975769043},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44841212034225464},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43261483311653137},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.412391722202301},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3948201537132263},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3668619394302368},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3605138957500458},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.339296817779541},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15209272503852844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12456250190734863},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10703009366989136},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10009780526161194},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07944920659065247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07855004072189331},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06758403778076172},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C70410870","wikidata":"https://www.wikidata.org/wiki/Q199906","display_name":"Clinical psychology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2017.2722417","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2017.2722417","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4c2db06033ee49c185b51659b9771186","is_oa":true,"landing_page_url":"https://doaj.org/article/4c2db06033ee49c185b51659b9771186","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 5, Pp 12224-12229 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2017.2722417","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2017.2722417","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2978788187","display_name":null,"funder_award_id":"LC201428","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"},{"id":"https://openalex.org/G437324850","display_name":null,"funder_award_id":"61573131","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323085","display_name":"Natural Science Foundation of Heilongjiang Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1986117210","https://openalex.org/W1995454290","https://openalex.org/W2077402293","https://openalex.org/W2084970142","https://openalex.org/W2098470425","https://openalex.org/W2104958104","https://openalex.org/W2116845400","https://openalex.org/W2154510168","https://openalex.org/W2164779921","https://openalex.org/W2166384194","https://openalex.org/W2178412471","https://openalex.org/W2248527772","https://openalex.org/W2485379754","https://openalex.org/W2512542300","https://openalex.org/W2579282996","https://openalex.org/W2795182086"],"related_works":["https://openalex.org/W1993510555","https://openalex.org/W4224312498","https://openalex.org/W1995649400","https://openalex.org/W1978738522","https://openalex.org/W1508583995","https://openalex.org/W2095028518","https://openalex.org/W2170091984","https://openalex.org/W2377228964","https://openalex.org/W2059311322","https://openalex.org/W2536963663"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,14,18,22,26,33,37,41,51,58,88,100],"stability":[4,15,35,67],"analysis":[5],"problem":[6],"for":[7],"planar":[8],"periodic":[9],"switching":[10],"systems.":[11],"We":[12],"characterize":[13],"margin":[16],"in":[17,40,54,71,87,96],"space":[19],"constituted":[20],"by":[21,28],"dwell":[23,52],"times":[24,53],"of":[25,36,60,63,73,76],"subsystems,":[27],"which":[29,79],"we":[30],"can":[31,80],"assess":[32],"asymptotic":[34],"overall":[38],"system":[39],"necessary":[42],"and":[43,84],"sufficient":[44],"sense.":[45],"The":[46,66],"mutual":[47],"constraint":[48],"conditions":[49,68],"on":[50,57],"nature":[55],"depend":[56],"type":[59],"equilibrium":[61],"point":[62],"each":[64],"subsystem.":[65],"are":[69],"expressed":[70],"terms":[72],"a":[74],"family":[75],"transcendental":[77],"inequalities,":[78],"be":[81],"numerically":[82],"solved":[83],"precisely":[85],"depicted":[86],"time-domain":[89],"space.":[90],"An":[91],"example":[92],"is":[93],"worked":[94],"out":[95],"detail":[97],"to":[98],"illustrate":[99],"theoretical":[101],"results.":[102]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}