{"id":"https://openalex.org/W2107132918","doi":"https://doi.org/10.1109/acc.2007.4282863","title":"A Novel Scheme for Positive Real Balanced Truncation","display_name":"A Novel Scheme for Positive Real Balanced Truncation","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2107132918","doi":"https://doi.org/10.1109/acc.2007.4282863","mag":"2107132918"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282863","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282863","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American 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/A5012239187","display_name":"Kari Unneland","orcid":null},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Kari Unneland","raw_affiliation_strings":["Department of Engineering Cybernetics(ITK), Norwegian University of Science and Technology, Trondheim, Norway","Norwegian Univ. of Sci. & Technol. NTNU, Trondheim"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Cybernetics(ITK), Norwegian University of Science and Technology, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]},{"raw_affiliation_string":"Norwegian Univ. of Sci. & Technol. NTNU, Trondheim","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036923077","display_name":"Paul Van Dooren","orcid":"https://orcid.org/0000-0002-0115-9932"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Paul Van Dooren","raw_affiliation_strings":["Department of Mathematical Engineering (INMA), Universite Catholique de Louvain, Louvain-la-Neuve, Belgium","Department of Mathematical Engineering (INMA), Universite Catholique de Louvain (UCL), 1348 Louvain la Neuve, Belgium. vdooren@csam.ucl.ac.be"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering (INMA), Universite Catholique de Louvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"Department of Mathematical Engineering (INMA), Universite Catholique de Louvain (UCL), 1348 Louvain la Neuve, Belgium. vdooren@csam.ucl.ac.be","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021192390","display_name":"Olav Egeland","orcid":"https://orcid.org/0000-0001-5472-9743"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Olav Egeland","raw_affiliation_strings":["Department of Engineering Cybernetics (ITK), Norwegian University of Science and Technology, Trondheim, Norway","Department of Engineering Cybernetics (ITK), Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway. olav.egeland@ntnu.no"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Cybernetics (ITK), Norwegian University of Science and Technology, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]},{"raw_affiliation_string":"Department of Engineering Cybernetics (ITK), Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway. olav.egeland@ntnu.no","institution_ids":["https://openalex.org/I204778367"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.14948454,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"947","last_page":"952"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9905999898910522,"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/riccati-equation","display_name":"Riccati equation","score":0.7958927154541016},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6565567255020142},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6091902256011963},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.6035770177841187},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5825167894363403},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5567135810852051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5068984627723694},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5038678050041199},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42869675159454346},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40839725732803345},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36152568459510803},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.190262109041214},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1296350657939911},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08688640594482422},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06788209080696106}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.7958927154541016},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6565567255020142},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6091902256011963},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.6035770177841187},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5825167894363403},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5567135810852051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5068984627723694},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5038678050041199},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42869675159454346},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40839725732803345},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36152568459510803},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.190262109041214},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1296350657939911},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08688640594482422},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06788209080696106},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2007.4282863","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282863","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311040","display_name":"Norges Teknisk-Naturvitenskapelige Universitet","ror":"https://ror.org/05xg72x27"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W220567546","https://openalex.org/W1551480811","https://openalex.org/W1570330619","https://openalex.org/W1965623622","https://openalex.org/W1968780839","https://openalex.org/W1984714339","https://openalex.org/W2034244658","https://openalex.org/W2037579718","https://openalex.org/W2040001778","https://openalex.org/W2064733273","https://openalex.org/W2071433326","https://openalex.org/W2095477585","https://openalex.org/W2121565841","https://openalex.org/W2125368842","https://openalex.org/W2155356103","https://openalex.org/W2541572255"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W2096105566","https://openalex.org/W1563296412","https://openalex.org/W2114791549","https://openalex.org/W2097622270","https://openalex.org/W2126205885","https://openalex.org/W2093841944"],"abstract_inverted_index":{"Here,":[0],"model":[1],"reduction,":[2],"based":[3],"on":[4],"balanced":[5,41],"truncation,":[6],"of":[7,19,52,66,118],"stable":[8],"and":[9,31,58,86],"passive":[10,74,96],"systems":[11],"will":[12,24,43],"be":[13,25,44],"considered.":[14],"An":[15],"overview":[16],"over":[17],"some":[18],"the":[20,53,64,79,111,115,119],"already":[21,54],"existing":[22,55],"techniques":[23],"given;":[26],"Lyapunov":[27,56,84],"balancing,":[28,63],"Riccati":[29,59,62,68,88],"balancing":[30,57],"Stochastic":[32],"balancing.":[33,60],"Subsequently":[34],"a":[35,50],"novel":[36],"scheme":[37],"for":[38],"positive":[39],"real":[40],"truncation":[42],"proposed.":[45],"This":[46],"new":[47],"method":[48],"is":[49,101,108],"combination":[51],"Using":[61],"solution":[65],"two":[67],"equations":[69],"are":[70,90],"needed":[71],"to":[72,94,113],"obtain":[73,95],"reduced":[75,97],"order":[76,93,98],"systems.":[77],"For":[78],"suggested":[80],"method,":[81],"only":[82],"one":[83,87],"equation":[85,89],"solved":[91],"in":[92],"systems,":[99],"which":[100],"less":[102],"computationally":[103],"demanding.":[104],"A":[105],"numerical":[106],"example":[107],"given":[109],"at":[110],"end":[112],"compare":[114],"approximation":[116],"error":[117],"different":[120],"schemes.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
