{"id":"https://openalex.org/W4232626294","doi":"https://doi.org/10.23919/ecc.1999.7099483","title":"The phenomenon of the higher order steady modes in the relay control systems with time delay","display_name":"The phenomenon of the higher order steady modes in the relay control systems with time delay","publication_year":1999,"publication_date":"1999-08-01","ids":{"openalex":"https://openalex.org/W4232626294","doi":"https://doi.org/10.23919/ecc.1999.7099483"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.1999.7099483","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7099483","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 European Control Conference (ECC)","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/A5007560074","display_name":"L. M. Pridman","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"L. M. Pridman","raw_affiliation_strings":["Dept. of Mathematics, Samara State Architecture and Civil Engineering Academy, 13-64 Gagarina str., Samara, 443079, Russia"],"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, Samara State Architecture and Civil Engineering Academy, 13-64 Gagarina str., Samara, 443079, Russia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007830129","display_name":"Emilia Fridman","orcid":"https://orcid.org/0000-0002-8773-9494"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"E. M. Fridman","raw_affiliation_strings":["Dept. of Electrical Engineering, Tel Aviv University, Ramat-Aviv, 69978 Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Dept. of Electrical Engineering, Tel Aviv University, Ramat-Aviv, 69978 Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010191901","display_name":"E. I. Shustin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153002","display_name":"American Friends of Tel Aviv University","ror":"https://ror.org/04dq3vj35","country_code":"US","type":"education","lineage":["https://openalex.org/I4210153002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. I. Shustin","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, IL"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, IL","institution_ids":["https://openalex.org/I4210153002"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007560074"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40388671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1259","last_page":"1264"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9771999716758728,"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"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.735611081123352},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6659812331199646},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6643440127372742},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.5249978303909302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5211167931556702},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5023994445800781},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5022799968719482},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.48526856303215027},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.4828979969024658},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4598864018917084},{"id":"https://openalex.org/keywords/critical-frequency","display_name":"Critical frequency","score":0.4438949227333069},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4241122007369995},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4238084852695465},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41876912117004395},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3081936836242676},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.25966301560401917},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18007203936576843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.168842613697052},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09224182367324829}],"concepts":[{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.735611081123352},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6659812331199646},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6643440127372742},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.5249978303909302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5211167931556702},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5023994445800781},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5022799968719482},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.48526856303215027},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.4828979969024658},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4598864018917084},{"id":"https://openalex.org/C87635042","wikidata":"https://www.wikidata.org/wiki/Q5186717","display_name":"Critical frequency","level":3,"score":0.4438949227333069},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4241122007369995},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4238084852695465},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41876912117004395},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3081936836242676},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.25966301560401917},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18007203936576843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.168842613697052},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09224182367324829},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C116403925","wikidata":"https://www.wikidata.org/wiki/Q162219","display_name":"Ionosphere","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.1999.7099483","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7099483","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 European Control Conference (ECC)","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2074717584","https://openalex.org/W4285551356","https://openalex.org/W327603423","https://openalex.org/W2057771841","https://openalex.org/W2072647272","https://openalex.org/W4246323976","https://openalex.org/W2541551113","https://openalex.org/W2897741391","https://openalex.org/W2984926096","https://openalex.org/W2389672489"],"abstract_inverted_index":{"The":[0,59,134],"higher":[1],"order":[2,17,34,174,196,217],"relay":[3,18,169,236],"control":[4,19,170,237],"systems":[5,20,171,199,238],"with":[6,21,72,91,126,216,239],"delay":[7,22],"(HORCSD)":[8],"in":[9,190,207,235],"the":[10,15,24,27,32,43,81,105,110,124,141,147,159,168,178,191,194,201,204,210,213,228],"input":[11],"are":[12,37,62,130,223],"considered.":[13],"For":[14],"second":[16,33,195,222],"(SORCSD)":[23],"notations":[25],"of":[26,45,49,70,109,123,140,146,172,181,193,203,218],"frequency,":[28],"oscillatory":[29,47,88],"solutions":[30,122],"and":[31,138,200],"steady":[35,82,93,107,144,165,205,233],"modes":[36,108,145,166,198,206,215,234],"introduced.":[38],"It":[39,95,113,153],"is":[40,79,96,114,151,154],"shown":[41,97,155],"that":[42,86,98,116,156,185],"frequency":[44,77,102,129,143,164,231],"any":[46,73,87,100,120,173],"solution":[48,69,89],"SORCSD":[50,71,125],"after":[51],"a":[52,57,68],"finite":[53],"time":[54],"interval":[55],"becomes":[56],"constant.":[58],"sufficient":[60],"conditions":[61,119],"found":[63],"under":[64,117],"which":[65,78],"there":[66,103,157,186,226],"exists":[67,187],"nonnegative":[74,101],"integer":[75],"constant":[76],"called":[80],"mode.":[83,94],"This":[84,183],"means":[85,184],"coincides":[90],"some":[92,118,188],"for":[99,167,177],"exist":[104,158,227],"periodic":[106,121,232],"autonomous":[111],"SORCSD.":[112,208],"justified":[115],"zero":[127,142,163,230],"limit":[128],"orbitally":[131,160],"asymptotically":[132,161],"stable.":[133],"theorem":[135],"about":[136],"existence":[137],"stability":[139],"singularly":[148],"perturbed":[149],"HORCSD":[150],"proved.":[152],"stable":[162,229],"at":[175],"list":[176],"small":[179],"value":[180],"parameter.":[182],"analogy":[189],"behavior":[192],"sliding":[197,214,219],"properties":[202],"From":[209],"other":[211],"hand":[212],"more":[220],"than":[221],"unstable":[224],"but":[225],"delay.":[240]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
