{"id":"https://openalex.org/W4399766508","doi":"https://doi.org/10.1109/tac.2024.3416322","title":"Comparison of Nondeterministic Stable Linear Systems by ($\\gamma,\\delta$)-Similarity","display_name":"Comparison of Nondeterministic Stable Linear Systems by ($\\gamma,\\delta$)-Similarity","publication_year":2024,"publication_date":"2024-06-18","ids":{"openalex":"https://openalex.org/W4399766508","doi":"https://doi.org/10.1109/tac.2024.3416322"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2024.3416322","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3416322","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":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/3a133441-8f3c-4848-82b4-e1d332252365","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051158060","display_name":"Armin Pirastehzad","orcid":"https://orcid.org/0000-0002-8238-7258"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Armin Pirastehzad","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, Netherlands","Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-8238-7258","affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005018540","display_name":"Arjan van der Schaft","orcid":"https://orcid.org/0000-0002-2383-9234"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Arjan van der Schaft","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, Netherlands","Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-2383-9234","affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083507299","display_name":"Bart Besselink","orcid":"https://orcid.org/0000-0001-5194-3306"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Bart Besselink","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, Netherlands","Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-5194-3306","affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I169381384"],"apc_list":null,"apc_paid":null,"fwci":0.2537,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54263867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"69","issue":"12","first_page":"8617","last_page":"8632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.7006000280380249,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.7006000280380249,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.6872000098228455,"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/T11236","display_name":"Control Systems and Identification","score":0.6665999889373779,"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/similarity","display_name":"Similarity (geometry)","score":0.5685722827911377},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5367200970649719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48836585879325867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3964836597442627},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38106369972229004},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36174097657203674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33990466594696045},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22408828139305115},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11825701594352722},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08778831362724304}],"concepts":[{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5685722827911377},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5367200970649719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48836585879325867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3964836597442627},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38106369972229004},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36174097657203674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33990466594696045},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22408828139305115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11825701594352722},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08778831362724304},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2024.3416322","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3416322","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:pure.rug.nl:openaire/3a133441-8f3c-4848-82b4-e1d332252365","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/3a133441-8f3c-4848-82b4-e1d332252365","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pirastehzad, A, van der Schaft, A & Besselink, B 2024, 'Comparison of Nondeterministic Stable Linear Systems by (\u03b3,\u03b4)-Similarity', IEEE Transactions on Automatic Control, vol. 69, no. 12, pp. 8617-8632. https://doi.org/10.1109/TAC.2024.3416322","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/3a133441-8f3c-4848-82b4-e1d332252365","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/3a133441-8f3c-4848-82b4-e1d332252365","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pirastehzad, A, van der Schaft, A & Besselink, B 2024, 'Comparison of Nondeterministic Stable Linear Systems by (\u03b3,\u03b4)-Similarity', IEEE Transactions on Automatic Control, vol. 69, no. 12, pp. 8617-8632. https://doi.org/10.1109/TAC.2024.3416322","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.rug.nl:publications/3a133441-8f3c-4848-82b4-e1d332252365","is_oa":true,"landing_page_url":"https://research.rug.nl/files/1209239993/Comparison_of_Nondeterministic_Stable_Linear_Systems_by_gammadelta-Similarity.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pirastehzad, A, van der Schaft, A & Besselink, B 2024, 'Comparison of Nondeterministic Stable Linear Systems by (\u03b3,\u03b4)-Similarity', IEEE Transactions on Automatic Control, vol. 69, no. 12, pp. 8617-8632. https://doi.org/10.1109/TAC.2024.3416322","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/3a133441-8f3c-4848-82b4-e1d332252365","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/3a133441-8f3c-4848-82b4-e1d332252365","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pirastehzad, A, van der Schaft, A & Besselink, B 2024, 'Comparison of Nondeterministic Stable Linear Systems by (\u03b3,\u03b4)-Similarity', IEEE Transactions on Automatic Control, vol. 69, no. 12, pp. 8617-8632. https://doi.org/10.1109/TAC.2024.3416322","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1503887525","https://openalex.org/W1927395284","https://openalex.org/W1973013779","https://openalex.org/W2011979623","https://openalex.org/W2025192585","https://openalex.org/W2066459185","https://openalex.org/W2074027094","https://openalex.org/W2090771707","https://openalex.org/W2095477585","https://openalex.org/W2109080678","https://openalex.org/W2117218135","https://openalex.org/W2118100616","https://openalex.org/W2127768514","https://openalex.org/W2164216842","https://openalex.org/W2228126549","https://openalex.org/W2487779201","https://openalex.org/W2536620281","https://openalex.org/W2565969279","https://openalex.org/W2571295681","https://openalex.org/W2762781394","https://openalex.org/W2765888560","https://openalex.org/W2808312533","https://openalex.org/W2962709723","https://openalex.org/W2964186632","https://openalex.org/W2964206241","https://openalex.org/W2967555261","https://openalex.org/W2969218722","https://openalex.org/W4205178436","https://openalex.org/W4214690803","https://openalex.org/W4248816015","https://openalex.org/W4253020970","https://openalex.org/W4315472297","https://openalex.org/W6684557030"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W1982160337","https://openalex.org/W2989452537","https://openalex.org/W1971380437","https://openalex.org/W1514662352"],"abstract_inverted_index":{"We":[0,101,160],"introduce":[1],"($\\gamma,\\delta$)-similarity,":[2],"a":[3,57,108],"notion":[4,58,104,134],"of":[5,33,43,66,78,93,105,120,129,155],"system":[6],"comparison":[7],"that":[8,59,132],"measures":[9],"to":[10,47],"what":[11],"extent":[12],"two":[13,38,49],"stable":[14],"linear":[15,109],"dynamical":[16,158],"systems":[17],"behave":[18],"similarly":[19],"in":[20,41,76,96,118,147,165],"an":[21,166],"input\u2013output":[22,61],"sense.":[23],"This":[24,142],"behavioral":[25],"similarity":[26],"is":[27,56,74,135],"characterized":[28],"by":[29],"measuring":[30],"the":[31,34,37,44,48,103,126,133],"sensitivity":[32],"difference":[35],"between":[36],"output":[39],"trajectories":[40],"terms":[42,77,119],"external":[45],"inputs":[46],"potentially":[50],"nondeterministic":[51],"systems.":[52,159],"As":[53],"such,":[54],"($\\gamma,\\delta$)-similarity":[55,82,106,130],"characterizesapproximationof":[60],"behavior,":[62],"whereas":[63],"existing":[64,87],"notions":[65],"simulation":[67],"target":[68],"equivalence.":[69],"Next,":[70],"as":[71,107],"this":[72],"approximation":[73],"specified":[75],"the$\\mathcal":[79],"{L}_{2}$signal":[80],"norm,":[81],"allows":[83],"for":[84,89],"integration":[85],"with":[86],"methods":[88],"analysis":[90],"and":[91,114,139,152],"synthesis":[92,154],"control":[94,99],"systems,":[95],"particular,":[97],"robust":[98],"techniques.":[100],"characterize":[102],"matrix":[110],"inequality":[111],"feasibility":[112],"problem":[113],"derive":[115],"its":[116,144],"interpretation":[117],"transfer":[121],"matrices.":[122],"Our":[123],"study":[124],"on":[125],"compositional":[127,148],"properties":[128],"shows":[131],"preserved":[136],"through":[137],"series":[138],"feedback":[140],"interconnections.":[141],"highlights":[143],"potential":[145],"application":[146],"reasoning,":[149],"namely":[150],"abstraction":[151],"modular":[153],"large-scale":[156],"interconnected":[157],"further":[161],"illustrate":[162],"our":[163],"results":[164],"electrical":[167],"network":[168],"example.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2024-06-19T00:00:00"}
