{"id":"https://openalex.org/W2025968708","doi":"https://doi.org/10.1080/00207170802460040","title":"On classical state space realisability of quadratic input\u2013output differential equations","display_name":"On classical state space realisability of quadratic input\u2013output differential equations","publication_year":2009,"publication_date":"2009-02-06","ids":{"openalex":"https://openalex.org/W2025968708","doi":"https://doi.org/10.1080/00207170802460040","mag":"2025968708"},"language":"en","primary_location":{"id":"doi:10.1080/00207170802460040","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170802460040","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-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/A5085233495","display_name":"\u00dclle Kotta","orcid":"https://orcid.org/0000-0002-7697-769X"},"institutions":[{"id":"https://openalex.org/I4210160054","display_name":"Cybernetica (Estonia)","ror":"https://ror.org/054gqc795","country_code":"EE","type":"company","lineage":["https://openalex.org/I4210160054"]}],"countries":["EE"],"is_corresponding":true,"raw_author_name":"\u00dc. Kotta","raw_affiliation_strings":["a  Institute of Cybernetics at TUT , Tallinn,  Estonia","Institute of Cybernetics at TUT , Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"a  Institute of Cybernetics at TUT , Tallinn,  Estonia","institution_ids":["https://openalex.org/I4210160054"]},{"raw_affiliation_string":"Institute of Cybernetics at TUT , Tallinn, Estonia","institution_ids":["https://openalex.org/I4210160054"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056423851","display_name":"P. Kotta","orcid":null},"institutions":[{"id":"https://openalex.org/I4210160054","display_name":"Cybernetica (Estonia)","ror":"https://ror.org/054gqc795","country_code":"EE","type":"company","lineage":["https://openalex.org/I4210160054"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"P. Kotta","raw_affiliation_strings":["a  Institute of Cybernetics at TUT , Tallinn,  Estonia","Institute of Cybernetics at TUT , Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"a  Institute of Cybernetics at TUT , Tallinn,  Estonia","institution_ids":["https://openalex.org/I4210160054"]},{"raw_affiliation_string":"Institute of Cybernetics at TUT , Tallinn, Estonia","institution_ids":["https://openalex.org/I4210160054"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067828156","display_name":"Maris T\u00f5nso","orcid":"https://orcid.org/0000-0002-7602-6544"},"institutions":[{"id":"https://openalex.org/I4210160054","display_name":"Cybernetica (Estonia)","ror":"https://ror.org/054gqc795","country_code":"EE","type":"company","lineage":["https://openalex.org/I4210160054"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"M. T\u00f5nso","raw_affiliation_strings":["a  Institute of Cybernetics at TUT , Tallinn,  Estonia","Institute of Cybernetics at TUT , Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"a  Institute of Cybernetics at TUT , Tallinn,  Estonia","institution_ids":["https://openalex.org/I4210160054"]},{"raw_affiliation_string":"Institute of Cybernetics at TUT , Tallinn, Estonia","institution_ids":["https://openalex.org/I4210160054"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113716034","display_name":"A.S.I. Zinober","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A.S.I. Zinober","raw_affiliation_strings":["b   Department of Applied Mathematics , The University of Sheffield , Sheffield,  UK","Department of Applied Mathematics , The University of Sheffield , Sheffield, UK"],"affiliations":[{"raw_affiliation_string":"b   Department of Applied Mathematics , The University of Sheffield , Sheffield,  UK","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Applied Mathematics , The University of Sheffield , Sheffield, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085233495"],"corresponding_institution_ids":["https://openalex.org/I4210160054"],"apc_list":null,"apc_paid":null,"fwci":0.7698,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76226727,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"82","issue":"7","first_page":"1212","last_page":"1218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9991999864578247,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9991999864578247,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9961000084877014,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9916999936103821,"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/quadratic-equation","display_name":"Quadratic equation","score":0.7681319713592529},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6743202805519104},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5510891675949097},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4988057613372803},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.49706533551216125},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.48233625292778015},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4367881417274475},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4361268877983093},{"id":"https://openalex.org/keywords/isotropic-quadratic-form","display_name":"Isotropic quadratic form","score":0.4330797791481018},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.3962705433368683},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38285842537879944},{"id":"https://openalex.org/keywords/binary-quadratic-form","display_name":"Binary quadratic form","score":0.23178181052207947},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1358291506767273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12474733591079712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11094453930854797}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7681319713592529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6743202805519104},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5510891675949097},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4988057613372803},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.49706533551216125},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.48233625292778015},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4367881417274475},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4361268877983093},{"id":"https://openalex.org/C21440807","wikidata":"https://www.wikidata.org/wiki/Q4968811","display_name":"Isotropic quadratic form","level":5,"score":0.4330797791481018},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.3962705433368683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38285842537879944},{"id":"https://openalex.org/C80695182","wikidata":"https://www.wikidata.org/wiki/Q864134","display_name":"Binary quadratic form","level":4,"score":0.23178181052207947},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1358291506767273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12474733591079712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11094453930854797},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207170802460040","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170802460040","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:10483","is_oa":false,"landing_page_url":"http://eprints.whiterose.ac.uk/10483/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W161760481","https://openalex.org/W1777498428","https://openalex.org/W2053879744","https://openalex.org/W2069199696","https://openalex.org/W2085742889","https://openalex.org/W2099679038","https://openalex.org/W2106641833","https://openalex.org/W2119982591","https://openalex.org/W2142076589","https://openalex.org/W2145434710","https://openalex.org/W2155931771","https://openalex.org/W2238816216","https://openalex.org/W3150565301","https://openalex.org/W4294183731"],"related_works":["https://openalex.org/W269925151","https://openalex.org/W4320232412","https://openalex.org/W4386731488","https://openalex.org/W4299819625","https://openalex.org/W2352916597","https://openalex.org/W2061663474","https://openalex.org/W2625742927","https://openalex.org/W2047406140","https://openalex.org/W108432118","https://openalex.org/W1578253330"],"abstract_inverted_index":{"This":[0],"article":[1],"studies":[2],"the":[3,13,20,23,51,65,73],"realisability":[4],"property":[5,66],"of":[6,22,37,50,70,72,97,101],"continuous-time":[7],"quadratic":[8,24,43,56,89,98],"input\u2013output":[9],"(i/o)":[10],"equations":[11,75,85,100],"in":[12],"classical":[14],"state":[15,84],"space":[16],"form.":[17],"Constraints":[18],"on":[19],"parameters":[21],"i/o":[25,42,55,74,90,99],"model":[26],"are":[27,58,76],"suggested":[28],"that":[29,67],"lead":[30],"to":[31],"realisable":[32,41,54,87,95],"models.":[33],"The":[34],"complete":[35],"list":[36],"second-":[38],"and":[39,47,92],"third-order":[40],"models":[44],"is":[45],"given":[46],"two":[48],"subclasses":[49],"n-th":[52],"order":[53],"systems":[57],"suggested.":[59],"Our":[60],"conditions":[61],"rely":[62],"basically":[63],"upon":[64],"certain":[68],"combinations":[69],"coefficients":[71],"zero":[77],"or":[78],"not":[79],"zero.":[80],"We":[81],"provide":[82],"explicit":[83],"for":[86,93],"second-order":[88],"equations,":[91],"one":[94],"subclass":[96],"arbitrary":[102],"order.":[103]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}