{"id":"https://openalex.org/W2088636284","doi":"https://doi.org/10.1137/080734200","title":"Positivity Preserving Balanced Truncation for Descriptor Systems","display_name":"Positivity Preserving Balanced Truncation for Descriptor Systems","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2088636284","doi":"https://doi.org/10.1137/080734200","mag":"2088636284"},"language":"en","primary_location":{"id":"doi:10.1137/080734200","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080734200","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5027602749","display_name":"Timo Reis","orcid":"https://orcid.org/0000-0003-0721-8494"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Timo Reis","raw_affiliation_strings":["[email\u00a0protected] and [email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected] and [email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060362561","display_name":"Elena Virnik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elena Virnik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9468,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.76408296,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"48","issue":"4","first_page":"2600","last_page":"2619"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9965000152587891,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9918000102043152,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9033766984939575},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.651053786277771},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5907250046730042},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5216115713119507},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.49100354313850403},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4751743674278259},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.43447068333625793},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4312896728515625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2298053801059723},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.081563800573349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0769166648387909},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07476049661636353},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06734773516654968}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9033766984939575},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.651053786277771},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5907250046730042},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5216115713119507},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.49100354313850403},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4751743674278259},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.43447068333625793},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4312896728515625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2298053801059723},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.081563800573349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0769166648387909},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07476049661636353},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06734773516654968},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080734200","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080734200","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5699999928474426,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W93591359","https://openalex.org/W151868298","https://openalex.org/W624020015","https://openalex.org/W1484944636","https://openalex.org/W1500921805","https://openalex.org/W1534430411","https://openalex.org/W1604304367","https://openalex.org/W1971453285","https://openalex.org/W1982798315","https://openalex.org/W1983490265","https://openalex.org/W1984714339","https://openalex.org/W1991579213","https://openalex.org/W2003137566","https://openalex.org/W2010362952","https://openalex.org/W2016031226","https://openalex.org/W2030348330","https://openalex.org/W2034493067","https://openalex.org/W2034786108","https://openalex.org/W2055581502","https://openalex.org/W2070623399","https://openalex.org/W2091991352","https://openalex.org/W2118255604","https://openalex.org/W2128834174","https://openalex.org/W2141548329","https://openalex.org/W2144326820","https://openalex.org/W2153132823","https://openalex.org/W2164127901","https://openalex.org/W2170831233","https://openalex.org/W2189057960","https://openalex.org/W2211802523","https://openalex.org/W2254131894","https://openalex.org/W2322753244","https://openalex.org/W3035235874","https://openalex.org/W3210839039","https://openalex.org/W4241143925","https://openalex.org/W4253629962"],"related_works":["https://openalex.org/W2038812594","https://openalex.org/W1672129608","https://openalex.org/W2139954142","https://openalex.org/W2963181540","https://openalex.org/W4299487705","https://openalex.org/W2579973725","https://openalex.org/W2734700240","https://openalex.org/W4296089997","https://openalex.org/W2378841998","https://openalex.org/W2884265924"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2],"model":[3],"reduction":[4],"method":[5],"for":[6,27],"positive":[7],"systems":[8],"that":[9],"ensures":[10],"the":[11,14,18,24,65],"positivity":[12],"of":[13,40],"reduced-order":[15],"model.":[16],"In":[17],"standard":[19],"as":[20,22],"well":[21],"in":[23,64],"descriptor":[25],"case,":[26],"continuous-time":[28],"and":[29,56,60],"discrete-time":[30],"systems,":[31],"our":[32],"approach":[33],"is":[34,67],"based":[35],"on":[36],"constructing":[37],"diagonal":[38],"solutions":[39],"Lyapunov":[41],"inequalities.":[42],"These":[43],"are":[44,50,58],"linear":[45],"matrix":[46],"inequalities":[47],"(LMIs),":[48],"which":[49],"shown":[51],"to":[52],"be":[53],"feasible.":[54],"Positivity":[55],"stability":[57],"preserved,":[59],"an":[61],"error":[62],"bound":[63],"$\\mathcal{H}_\\infty$-norm":[66],"provided.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
