{"id":"https://openalex.org/W1967109937","doi":"https://doi.org/10.1080/00207170701516389","title":"Frequency domain analysis for non-linear Volterra systems with a general non-linear output function","display_name":"Frequency domain analysis for non-linear Volterra systems with a general non-linear output function","publication_year":2007,"publication_date":"2007-11-16","ids":{"openalex":"https://openalex.org/W1967109937","doi":"https://doi.org/10.1080/00207170701516389","mag":"1967109937"},"language":"en","primary_location":{"id":"doi:10.1080/00207170701516389","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701516389","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/A5071742051","display_name":"Xingjian Jing","orcid":"https://orcid.org/0000-0003-3498-2180"},"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":true,"raw_author_name":"X. J. Jing","raw_affiliation_strings":["University of Sheffield","Department of Automatic Control and Systems Engineering, University of Sheffield. Mappin Street, Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"University of Sheffield","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield. Mappin Street, Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091158145","display_name":"Zi\u2013Qiang Lang","orcid":"https://orcid.org/0000-0003-3598-089X"},"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":"Z. Q. Lang","raw_affiliation_strings":["University of Sheffield","Department of Automatic Control and Systems Engineering, University of Sheffield. Mappin Street, Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"University of Sheffield","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield. Mappin Street, Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105466125","display_name":"S.A. Billings","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":"S. A. Billings","raw_affiliation_strings":["University of Sheffield","Department of Automatic Control and Systems Engineering, University of Sheffield. Mappin Street, Sheffield, S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"University of Sheffield","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield. Mappin Street, Sheffield, S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071742051"],"corresponding_institution_ids":["https://openalex.org/I91136226"],"apc_list":null,"apc_paid":null,"fwci":3.4837,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.9234146,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"81","issue":"2","first_page":"235","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9998999834060669,"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/T11236","display_name":"Control Systems and Identification","score":0.9998999834060669,"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":0.9930999875068665,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/frequency-response","display_name":"Frequency response","score":0.7362150549888611},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.6508374810218811},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5923976898193359},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5478826761245728},{"id":"https://openalex.org/keywords/describing-function","display_name":"Describing function","score":0.48640015721321106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48616310954093933},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44768691062927246},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.4382193088531494},{"id":"https://openalex.org/keywords/volterra-series","display_name":"Volterra series","score":0.4284232556819916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40557220578193665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3440197706222534},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2702495753765106},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22055485844612122},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.17861658334732056},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14712625741958618},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.10309863090515137},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08983829617500305}],"concepts":[{"id":"https://openalex.org/C8590192","wikidata":"https://www.wikidata.org/wiki/Q1054694","display_name":"Frequency response","level":2,"score":0.7362150549888611},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.6508374810218811},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5923976898193359},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5478826761245728},{"id":"https://openalex.org/C147317941","wikidata":"https://www.wikidata.org/wiki/Q1925419","display_name":"Describing function","level":3,"score":0.48640015721321106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48616310954093933},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44768691062927246},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.4382193088531494},{"id":"https://openalex.org/C2778532037","wikidata":"https://www.wikidata.org/wiki/Q3957891","display_name":"Volterra series","level":3,"score":0.4284232556819916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40557220578193665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3440197706222534},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2702495753765106},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22055485844612122},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.17861658334732056},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14712625741958618},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.10309863090515137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08983829617500305},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207170701516389","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701516389","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.soton.ac.uk:65337","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/65337/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"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":[{"id":"https://openalex.org/G4640399991","display_name":null,"funder_award_id":"EP/F017715/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W248160023","https://openalex.org/W256510569","https://openalex.org/W1597839575","https://openalex.org/W1615672776","https://openalex.org/W1967358568","https://openalex.org/W1968309948","https://openalex.org/W1968996649","https://openalex.org/W1979071895","https://openalex.org/W1997629775","https://openalex.org/W2017990884","https://openalex.org/W2019865578","https://openalex.org/W2028847290","https://openalex.org/W2034086315","https://openalex.org/W2037618134","https://openalex.org/W2043151544","https://openalex.org/W2074872635","https://openalex.org/W2115313921","https://openalex.org/W2124904508","https://openalex.org/W2134476339","https://openalex.org/W2141853751","https://openalex.org/W2160068178","https://openalex.org/W2167101944","https://openalex.org/W2169745860","https://openalex.org/W4238935570"],"related_works":["https://openalex.org/W2060656643","https://openalex.org/W2006936312","https://openalex.org/W613610909","https://openalex.org/W2405411269","https://openalex.org/W1964628732","https://openalex.org/W2120101598","https://openalex.org/W3208378821","https://openalex.org/W2074400455","https://openalex.org/W2079557485","https://openalex.org/W4239730234"],"abstract_inverted_index":{"For":[0],"non-linear":[1,7,13,47],"Volterra":[2],"systems":[3,48],"which":[4],"include":[5],"a":[6,11],"state":[8],"equation":[9],"and":[10,21,29,54,65,69,75],"general":[12,44],"output":[14],"function,":[15],"the":[16,38,60,70,76,89],"system":[17],"frequency":[18,24,39,66,80],"response":[19,25,40,67,81],"functions":[20,41],"some":[22,51],"related":[23],"characteristics":[26],"are":[27,85],"developed":[28],"discussed":[30],"in":[31],"this":[32,43],"study.":[33],"These":[34],"new":[35,90],"results":[36],"establish":[37],"for":[42],"form":[45],"of":[46,79],"by":[49],"extending":[50],"existing":[52],"theory,":[53],"provide":[55],"an":[56],"analytical":[57],"insight":[58],"into":[59],"relationship":[61,71],"between":[62,72],"model":[63,73],"parameters":[64,74],"functions,":[68],"magnitude":[77],"bound":[78],"functions.":[82],"Several":[83],"examples":[84],"given":[86],"to":[87],"illustrate":[88],"results.":[91]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}