{"id":"https://openalex.org/W2016348017","doi":"https://doi.org/10.1109/cca.2012.6402403","title":"Explicit formulas for the state coordinates in nonlinear MIMO realization problem on homogeneous time scales","display_name":"Explicit formulas for the state coordinates in nonlinear MIMO realization problem on homogeneous time scales","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W2016348017","doi":"https://doi.org/10.1109/cca.2012.6402403","mag":"2016348017"},"language":"en","primary_location":{"id":"doi:10.1109/cca.2012.6402403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2012.6402403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Control Applications","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/A5043375178","display_name":"Juri Belikov","orcid":"https://orcid.org/0000-0002-8243-7374"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Juri Belikov","raw_affiliation_strings":["Institute of Cybernetics, Tallinn University of Technology, Tallinn, Estonia","Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Cybernetics, Tallinn University of Technology, Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]},{"raw_affiliation_string":"Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Estonia","institution_ids":["https://openalex.org/I111112146"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085233495","display_name":"\u00dclle Kotta","orcid":"https://orcid.org/0000-0002-7697-769X"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Ulle Kotta","raw_affiliation_strings":["Institute of Cybernetics, Tallinn University of Technology, Tallinn, Estonia","Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Cybernetics, Tallinn University of Technology, Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]},{"raw_affiliation_string":"Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Estonia","institution_ids":["https://openalex.org/I111112146"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067828156","display_name":"Maris T\u00f5nso","orcid":"https://orcid.org/0000-0002-7602-6544"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Maris Tonso","raw_affiliation_strings":["Institute of Cybernetics, Tallinn University of Technology, Tallinn, Estonia","Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Cybernetics, Tallinn University of Technology, Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]},{"raw_affiliation_string":"Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Estonia","institution_ids":["https://openalex.org/I111112146"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1369,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.81802078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"56","issue":null,"first_page":"1388","last_page":"1393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9800999760627747,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9800999760627747,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9799000024795532,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9657999873161316,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/realization","display_name":"Realization (probability)","score":0.8364861011505127},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6467646360397339},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.5819398760795593},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5784732699394226},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.5648224949836731},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5528308749198914},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5005569458007812},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4825391173362732},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4635296165943146},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.43401217460632324},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.4134174883365631},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41108131408691406},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4106450378894806},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3761170506477356},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33099135756492615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25541311502456665},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19196456670761108}],"concepts":[{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.8364861011505127},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6467646360397339},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.5819398760795593},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5784732699394226},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.5648224949836731},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5528308749198914},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5005569458007812},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4825391173362732},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4635296165943146},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.43401217460632324},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4134174883365631},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41108131408691406},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4106450378894806},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3761170506477356},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33099135756492615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25541311502456665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19196456670761108},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cca.2012.6402403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2012.6402403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Control Applications","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323438","display_name":"Tallinna Tehnika\u00fclikool","ror":"https://ror.org/0443cwa12"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W271810198","https://openalex.org/W1596655614","https://openalex.org/W1973681634","https://openalex.org/W1998233083","https://openalex.org/W2016868638","https://openalex.org/W2063222672","https://openalex.org/W2080602599","https://openalex.org/W2082472945","https://openalex.org/W2158468751","https://openalex.org/W2160707881","https://openalex.org/W2182091239","https://openalex.org/W2577779281","https://openalex.org/W6643858822","https://openalex.org/W6649684858","https://openalex.org/W6654463825","https://openalex.org/W6686304304"],"related_works":["https://openalex.org/W4290802965","https://openalex.org/W97789383","https://openalex.org/W3087516072","https://openalex.org/W2727156679","https://openalex.org/W4289406402","https://openalex.org/W3213353046","https://openalex.org/W2912656129","https://openalex.org/W3088932775","https://openalex.org/W2606484672","https://openalex.org/W2148256306"],"abstract_inverted_index":{"The":[0,20],"problem":[1],"of":[2,4,27,41,51,61],"realization":[3],"nonlinear":[5],"multi-input":[6],"multi-output":[7],"equations,":[8],"defined":[9],"on":[10,24,38],"homogeneous":[11],"time":[12],"scale,":[13],"in":[14,65],"the":[15,33,49,52,62,66],"state-space":[16],"form":[17],"is":[18],"studied.":[19],"polynomial":[21],"approach,":[22],"based":[23,37],"non-commutative":[25],"ring":[26],"skew":[28],"polynomials,":[29],"allows":[30],"to":[31,47],"replace":[32],"existing":[34],"step-by-step":[35],"algorithm":[36],"certain":[39],"sequences":[40],"differential":[42],"one-forms":[43],"by":[44],"explicit":[45],"formulas":[46],"compute":[48],"differentials":[50],"state":[53],"coordinates":[54],"directly":[55],"from":[56],"system":[57],"description.":[58],"Implementation":[59],"details":[60],"developed":[63],"theory":[64],"Mathematica":[67],"environment":[68],"are":[69],"presented.":[70]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
