{"id":"https://openalex.org/W2025587640","doi":"https://doi.org/10.1109/mmar.2012.6347922","title":"New frequency domain based stability tests for 2D linear systems","display_name":"New frequency domain based stability tests for 2D linear systems","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2025587640","doi":"https://doi.org/10.1109/mmar.2012.6347922","mag":"2025587640"},"language":"en","primary_location":{"id":"doi:10.1109/mmar.2012.6347922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mmar.2012.6347922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 17th International Conference on Methods &amp; Models in Automation &amp; Robotics (MMAR)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5017767595","display_name":"Wojciech Paszke","orcid":"https://orcid.org/0000-0001-5060-0993"},"institutions":[{"id":"https://openalex.org/I46305939","display_name":"University of Zielona G\u00f3ra","ror":"https://ror.org/04fzm7v55","country_code":"PL","type":"education","lineage":["https://openalex.org/I46305939"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Wojciech Paszke","raw_affiliation_strings":["Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, Zielona Gora, Poland","Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, ul. Podg\u00f3rna 50, 65-246 Zielona G\u00f2ra, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, Zielona Gora, Poland","institution_ids":["https://openalex.org/I46305939"]},{"raw_affiliation_string":"Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, ul. Podg\u00f3rna 50, 65-246 Zielona G\u00f2ra, Poland","institution_ids":["https://openalex.org/I46305939"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081788754","display_name":"Eric Rogers","orcid":"https://orcid.org/0000-0003-0179-9398"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Eric Rogers","raw_affiliation_strings":["School of Electronics and Computer Science, University of Southampton, Southampton, UK","School of Electronics and Computer Science University of Southampton, Southampton SO17 1BJ UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronics and Computer Science, University of Southampton, Southampton, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"School of Electronics and Computer Science University of Southampton, Southampton SO17 1BJ UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089562946","display_name":"Paolo Rapisarda","orcid":"https://orcid.org/0000-0001-9682-8977"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paolo Rapisarda","raw_affiliation_strings":["School of Electronics and Computer Science, University of Southampton, Southampton, UK","School of Electronics and Computer Science University of Southampton, Southampton SO17 1BJ UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronics and Computer Science, University of Southampton, Southampton, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"School of Electronics and Computer Science University of Southampton, Southampton SO17 1BJ UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066492464","display_name":"Krzysztof Ga\u0142kowski","orcid":"https://orcid.org/0000-0003-4470-2162"},"institutions":[{"id":"https://openalex.org/I46305939","display_name":"University of Zielona G\u00f3ra","ror":"https://ror.org/04fzm7v55","country_code":"PL","type":"education","lineage":["https://openalex.org/I46305939"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Galkowski","raw_affiliation_strings":["Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, ul. Podg\u00f3rna 50, 65-246 Zielona G\u00f2ra, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Control and Computation Engineering, University of Zielona G\u00f3ra, ul. Podg\u00f3rna 50, 65-246 Zielona G\u00f2ra, Poland","institution_ids":["https://openalex.org/I46305939"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080666933","display_name":"Anton Kummert","orcid":"https://orcid.org/0000-0002-0282-5087"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anton Kummert","raw_affiliation_strings":["Faculty of Electrical, Information and Media Engineering, Communication Theory, University of Wuppertal, Wuppertal, Germany","University of Wuppertal, Faculty of Electrical, Information and Media Engineering, Communication Theory. Wuppertal, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical, Information and Media Engineering, Communication Theory, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"University of Wuppertal, Faculty of Electrical, Information and Media Engineering, Communication Theory. Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"349","issue":null,"first_page":"9","last_page":"14"},"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":1.0,"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":1.0,"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":0.9988999962806702,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.998199999332428,"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/lemma","display_name":"Lemma (botany)","score":0.6875424981117249},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.6290113925933838},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.5718035101890564},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.56620192527771},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5632362365722656},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5473359823226929},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.5453299283981323},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5382636785507202},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.52993243932724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.518624484539032},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4597698450088501},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.44608041644096375},{"id":"https://openalex.org/keywords/multidimensional-systems","display_name":"Multidimensional systems","score":0.4216655492782593},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4052457809448242},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35109269618988037},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3342999219894409},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19725683331489563},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16058394312858582},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14835718274116516},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11613935232162476}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6875424981117249},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.6290113925933838},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.5718035101890564},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.56620192527771},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5632362365722656},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5473359823226929},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.5453299283981323},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5382636785507202},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.52993243932724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.518624484539032},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4597698450088501},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.44608041644096375},{"id":"https://openalex.org/C158457486","wikidata":"https://www.wikidata.org/wiki/Q17104301","display_name":"Multidimensional systems","level":2,"score":0.4216655492782593},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4052457809448242},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35109269618988037},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3342999219894409},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19725683331489563},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16058394312858582},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14835718274116516},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11613935232162476},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/mmar.2012.6347922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mmar.2012.6347922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 17th International Conference on Methods &amp; Models in Automation &amp; Robotics (MMAR)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W130632564","https://openalex.org/W1003002143","https://openalex.org/W1482504246","https://openalex.org/W1485871597","https://openalex.org/W1530768209","https://openalex.org/W1668151268","https://openalex.org/W1971016989","https://openalex.org/W2004080117","https://openalex.org/W2026196308","https://openalex.org/W2029483576","https://openalex.org/W2031993719","https://openalex.org/W2051222277","https://openalex.org/W2053863919","https://openalex.org/W2057673261","https://openalex.org/W2074217064","https://openalex.org/W2081138225","https://openalex.org/W2100038940","https://openalex.org/W2108489060","https://openalex.org/W2127623647","https://openalex.org/W2157192413","https://openalex.org/W4254709818","https://openalex.org/W6605250307"],"related_works":["https://openalex.org/W2060195842","https://openalex.org/W2020788389","https://openalex.org/W2147442790","https://openalex.org/W2379295215","https://openalex.org/W4728229","https://openalex.org/W2089102366","https://openalex.org/W4387410785","https://openalex.org/W2045015574","https://openalex.org/W2347536774","https://openalex.org/W1996579463"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"a":[3,38],"new":[4],"set":[5],"of":[6,12,26,37],"stability":[7,11],"conditions":[8,50],"for":[9],"asymptotic":[10],"two-dimensional":[13],"linear":[14,43],"systems":[15],"described":[16],"by":[17],"Roesser":[18],"and":[19],"Fornasini-Marchesini":[20],"state-space":[21],"models":[22],"through":[23],"extensive":[24],"use":[25],"the":[27,48],"Kalman-Yakubovich-Popov":[28],"lemma.":[29],"The":[30],"resulting":[31,49],"tests":[32],"are":[33,82],"formulated":[34],"in":[35],"terms":[36],"convex":[39],"optimization":[40],"problem":[41],"over":[42],"matrix":[44],"inequality":[45],"constraints.":[46],"Testing":[47],"only":[51],"requires":[52],"computations":[53],"on":[54],"matrices":[55],"with":[56,59,66],"constant":[57],"entries":[58],"consequent":[60],"computational":[61],"load":[62],"advantages":[63],"when":[64,69],"compared":[65],"alternatives,":[67],"especially":[68],"direct":[70],"extension":[71],"to":[72],"stabilizing":[73],"control":[74],"law":[75],"design":[76],"is":[77],"required.":[78],"Illustrative":[79],"numerical":[80],"examples":[81],"also":[83],"given.":[84]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
