{"id":"https://openalex.org/W2009390584","doi":"https://doi.org/10.1109/cdc.2011.6160707","title":"Root locus for SISO infinite-dimensional systems","display_name":"Root locus for SISO infinite-dimensional systems","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2009390584","doi":"https://doi.org/10.1109/cdc.2011.6160707","mag":"2009390584"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160707","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160707","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","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/A5082176398","display_name":"Birgit Jacob","orcid":"https://orcid.org/0000-0002-8775-4424"},"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":true,"raw_author_name":"Birgit Jacob","raw_affiliation_strings":["Faculty of Mathematics und Natural Sciences, University of Wuppertal, Wuppertal, Germany","Faculty of Mathematics und Natural Sciences, University of Wuppertal, Gau\u00dfstra\u00dfe 20, 42119, GERMANY"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics und Natural Sciences, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Faculty of Mathematics und Natural Sciences, University of Wuppertal, Gau\u00dfstra\u00dfe 20, 42119, GERMANY","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049638450","display_name":"Kirsten Morris","orcid":"https://orcid.org/0000-0003-1311-9230"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Kirsten Morris","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","Dept. of Applied Mathematics, University of Waterloo, ON N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Dept. of Applied Mathematics, University of Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082176398"],"corresponding_institution_ids":["https://openalex.org/I167360494"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.07473737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"194","issue":null,"first_page":"1999","last_page":"2003"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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/T10046","display_name":"Stability and Control of Uncertain 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/root-locus","display_name":"Root locus","score":0.878574550151825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6211112141609192},{"id":"https://openalex.org/keywords/pole\u2013zero-plot","display_name":"Pole\u2013zero plot","score":0.561369776725769},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4761105477809906},{"id":"https://openalex.org/keywords/locus","display_name":"Locus (genetics)","score":0.4745294153690338},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46852463483810425},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.46762901544570923},{"id":"https://openalex.org/keywords/interlacing","display_name":"Interlacing","score":0.4651205539703369},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4513789415359497},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4141704738140106},{"id":"https://openalex.org/keywords/distributed-parameter-system","display_name":"Distributed parameter system","score":0.41357800364494324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37085622549057007},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.18914112448692322},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1884635090827942}],"concepts":[{"id":"https://openalex.org/C27162326","wikidata":"https://www.wikidata.org/wiki/Q957693","display_name":"Root locus","level":3,"score":0.878574550151825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6211112141609192},{"id":"https://openalex.org/C43656286","wikidata":"https://www.wikidata.org/wiki/Q2100961","display_name":"Pole\u2013zero plot","level":3,"score":0.561369776725769},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4761105477809906},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.4745294153690338},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46852463483810425},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.46762901544570923},{"id":"https://openalex.org/C95439218","wikidata":"https://www.wikidata.org/wiki/Q1666173","display_name":"Interlacing","level":2,"score":0.4651205539703369},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4513789415359497},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4141704738140106},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.41357800364494324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37085622549057007},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.18914112448692322},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1884635090827942},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6160707","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160707","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1538686203","https://openalex.org/W1552202016","https://openalex.org/W1562265198","https://openalex.org/W1574617701","https://openalex.org/W1575147392","https://openalex.org/W1606157354","https://openalex.org/W1974113123","https://openalex.org/W2009228623","https://openalex.org/W2019711277","https://openalex.org/W2056409570","https://openalex.org/W2098081686","https://openalex.org/W2133379892","https://openalex.org/W2150663223","https://openalex.org/W2525143841","https://openalex.org/W2592612214","https://openalex.org/W2730533933","https://openalex.org/W3144829920","https://openalex.org/W3151443225","https://openalex.org/W4205365047","https://openalex.org/W6740657130"],"related_works":["https://openalex.org/W2766948293","https://openalex.org/W2140634538","https://openalex.org/W2139448165","https://openalex.org/W1905800670","https://openalex.org/W615774510","https://openalex.org/W2049192849","https://openalex.org/W2538906928","https://openalex.org/W2091656199","https://openalex.org/W2071641368","https://openalex.org/W2166625018"],"abstract_inverted_index":{"The":[0],"root":[1,62,89],"locus":[2,63,90],"is":[3,24,68,91],"an":[4,42],"important":[5],"tool":[6],"for":[7,70,78,104,116],"analysing":[8],"the":[9,22,61,88,95,111],"stability":[10],"and":[11,45,64],"time":[12],"constants":[13],"of":[14,60,74,84,87],"linear":[15],"finite-dimensional":[16,79,105],"systems":[17,28,39,118],"as":[18],"a":[19,57,71,85,92,121],"parameter,":[20],"often":[21],"gain,":[23],"varied.":[25],"However,":[26,94],"many":[27],"are":[29,49],"modelled":[30],"by":[31,120],"partial":[32],"differential":[33],"equations":[34],"or":[35],"delay":[36],"equations.":[37],"These":[38],"evolve":[40],"on":[41],"infinite-dimensional":[43,75,126],"space":[44],"their":[46],"transfer":[47],"functions":[48],"not":[50],"rational.":[51],"In":[52],"this":[53],"paper":[54],"we":[55],"provide":[56],"rigorous":[58],"definition":[59],"show":[65,109],"that":[66,103,110],"it":[67],"well-defined":[69],"large":[72],"class":[73],"systems.":[76,106,127],"As":[77],"systems,":[80],"any":[81],"limit":[82],"point":[83],"branch":[86],"zero.":[93],"asymptotic":[96],"behaviour":[97],"can":[98],"be":[99],"quite":[100],"different":[101],"from":[102],"We":[107],"also":[108],"familar":[112],"pole-zero":[113],"interlacing":[114],"property":[115],"collocated":[117],"generated":[119],"self-adjoint":[122],"operator":[123],"extends":[124],"to":[125]},"counts_by_year":[{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}