{"id":"https://openalex.org/W3045860547","doi":"https://doi.org/10.3390/sym12081241","title":"The Problem of Invariance in Nonlinear Discrete-Time Dynamic Systems","display_name":"The Problem of Invariance in Nonlinear Discrete-Time Dynamic Systems","publication_year":2020,"publication_date":"2020-07-28","ids":{"openalex":"https://openalex.org/W3045860547","doi":"https://doi.org/10.3390/sym12081241","mag":"3045860547"},"language":"en","primary_location":{"id":"doi:10.3390/sym12081241","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081241","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1241/pdf?version=1595922710","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/8/1241/pdf?version=1595922710","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061015204","display_name":"Alexey Zhirabok","orcid":"https://orcid.org/0000-0001-5927-7117"},"institutions":[{"id":"https://openalex.org/I204947315","display_name":"Far Eastern Federal University","ror":"https://ror.org/0412y9z21","country_code":"RU","type":"education","lineage":["https://openalex.org/I204947315"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Alexey Zhirabok","raw_affiliation_strings":["Department of Automation and Control, Far Eastern Federal University, 690095 Vladivostok, Russia"],"raw_orcid":"https://orcid.org/0000-0001-5927-7117","affiliations":[{"raw_affiliation_string":"Department of Automation and Control, Far Eastern Federal University, 690095 Vladivostok, Russia","institution_ids":["https://openalex.org/I204947315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061015204"],"corresponding_institution_ids":["https://openalex.org/I204947315"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2977,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55418711,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"8","first_page":"1241","last_page":"1241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9991000294685364,"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":0.9991000294685364,"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/T14470","display_name":"Advanced Data Processing Techniques","score":0.9973999857902527,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9797999858856201,"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/decoupling","display_name":"Decoupling (probability)","score":0.6544281244277954},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6212279200553894},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6050333380699158},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4879903197288513},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4856039881706238},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4785900115966797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.429750919342041},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3960462808609009},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3933351933956146},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3583414554595947},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.23037755489349365},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2153976559638977},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.11864522099494934},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09476009011268616},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07146114110946655}],"concepts":[{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.6544281244277954},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6212279200553894},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6050333380699158},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4879903197288513},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4856039881706238},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4785900115966797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.429750919342041},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3960462808609009},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3933351933956146},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3583414554595947},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.23037755489349365},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2153976559638977},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.11864522099494934},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09476009011268616},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07146114110946655},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12081241","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081241","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1241/pdf?version=1595922710","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fc1cd70b815446c3aaeab05b1f2097c7","is_oa":true,"landing_page_url":"https://doaj.org/article/fc1cd70b815446c3aaeab05b1f2097c7","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":"Symmetry, Vol 12, Iss 8, p 1241 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/8/1241/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12081241","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12081241","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081241","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1241/pdf?version=1595922710","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4000000059604645}],"awards":[{"id":"https://openalex.org/G3141717737","display_name":null,"funder_award_id":"16-19-00046-P","funder_id":"https://openalex.org/F4320311239","funder_display_name":"Russian Science Support Foundation"}],"funders":[{"id":"https://openalex.org/F4320311239","display_name":"Russian Science Support Foundation","ror":"https://ror.org/005t0n560"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3045860547.pdf","grobid_xml":"https://content.openalex.org/works/W3045860547.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W580979487","https://openalex.org/W1556970733","https://openalex.org/W1793079058","https://openalex.org/W1859375249","https://openalex.org/W1998112257","https://openalex.org/W2030024491","https://openalex.org/W2036005612","https://openalex.org/W2042453974","https://openalex.org/W2050112382","https://openalex.org/W2066729921","https://openalex.org/W2085742889","https://openalex.org/W2100626771","https://openalex.org/W2112381154","https://openalex.org/W2127951847","https://openalex.org/W2145539240","https://openalex.org/W2161789438","https://openalex.org/W2408430026","https://openalex.org/W2494112937","https://openalex.org/W2537335803","https://openalex.org/W2735466230","https://openalex.org/W2938922387","https://openalex.org/W3011531283","https://openalex.org/W3160954918","https://openalex.org/W4292872153","https://openalex.org/W4294183731"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W4313561376","https://openalex.org/W3103825105","https://openalex.org/W3181683615","https://openalex.org/W3027880158","https://openalex.org/W3207533102","https://openalex.org/W1617565119"],"abstract_inverted_index":{"The":[0],"paper":[1],"considers":[2],"the":[3,10,20,22,40,52,60],"problem":[4,53],"of":[5,27,39,50,69],"invariance":[6,71],"with":[7],"respect":[8],"to":[9],"unknown":[11],"input":[12],"for":[13],"discrete-time":[14],"nonlinear":[15],"dynamic":[16],"systems.":[17],"To":[18],"solve":[19],"problem,":[21,79],"algebraic":[23],"approaches,":[24],"called":[25],"algebra":[26],"functions":[28,62],"and":[29,47,63,75,80],"logic\u2013dynamic":[30],"approach,":[31],"are":[32,54,65,83],"used.":[33],"Such":[34],"approaches":[35],"assume":[36],"that":[37],"description":[38],"system":[41],"may":[42],"contain":[43],"non-differentiable":[44],"functions.":[45],"Necessary":[46],"sufficient":[48],"conditions":[49],"solvability":[51],"obtained.":[55],"Moreover,":[56],"procedures":[57],"which":[58],"find":[59],"appropriate":[61],"matrices":[64],"developed.":[66],"Some":[67],"applications":[68],"such":[70],"in":[72],"fault":[73],"detection":[74],"isolation,":[76],"disturbance":[77],"decoupling":[78],"fault-tolerant":[81],"control":[82],"considered.":[84]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
