{"id":"https://openalex.org/W2009762405","doi":"https://doi.org/10.1109/9.544000","title":"Balancing and model reduction for second-order form linear systems","display_name":"Balancing and model reduction for second-order form linear systems","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2009762405","doi":"https://doi.org/10.1109/9.544000","mag":"2009762405"},"language":"en","primary_location":{"id":"doi:10.1109/9.544000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/9.544000","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic 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/A5111715005","display_name":"D.G. Meyer","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D.G. Meyer","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of Colorado, Boulder, CO, USA","[Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA]"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"[Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA]","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064210811","display_name":"Sriram Srinivasan","orcid":"https://orcid.org/0000-0002-4027-532X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Srinivasan","raw_affiliation_strings":["United Technologies Research Center, Inc., Hartford, CT, USA","[United Technologies Research Center, Inc., Hartford, CT, USA]"],"affiliations":[{"raw_affiliation_string":"United Technologies Research Center, Inc., Hartford, CT, USA","institution_ids":[]},{"raw_affiliation_string":"[United Technologies Research Center, Inc., Hartford, CT, USA]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111715005"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":1.3865,"has_fulltext":false,"cited_by_count":155,"citation_normalized_percentile":{"value":0.79750899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"41","issue":"11","first_page":"1632","last_page":"1644"},"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":0.9864000082015991,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/reduction","display_name":"Reduction (mathematics)","score":0.8105019330978394},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.6499221920967102},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5812594294548035},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5610830783843994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.530784010887146},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4408486485481262},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4350031316280365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42637547850608826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34189572930336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3400474190711975},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17128238081932068},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0911974310874939},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07340481877326965}],"concepts":[{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.8105019330978394},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.6499221920967102},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5812594294548035},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5610830783843994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.530784010887146},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4408486485481262},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4350031316280365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42637547850608826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34189572930336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3400474190711975},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17128238081932068},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0911974310874939},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07340481877326965},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/9.544000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/9.544000","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1856635350","https://openalex.org/W1984714339","https://openalex.org/W2000839177","https://openalex.org/W2064733273","https://openalex.org/W2079665343","https://openalex.org/W2099180896","https://openalex.org/W2114044578","https://openalex.org/W2129736406","https://openalex.org/W2791719834","https://openalex.org/W3143092787"],"related_works":["https://openalex.org/W2765250005","https://openalex.org/W2110312969","https://openalex.org/W2182451763","https://openalex.org/W2153566364","https://openalex.org/W1991018216","https://openalex.org/W2118904547","https://openalex.org/W2015479478","https://openalex.org/W3127703504","https://openalex.org/W1964286429","https://openalex.org/W2800915648"],"abstract_inverted_index":{"Model":[0],"reduction":[1,21,38,92],"of":[2],"second-order":[3,11,35,60,70,80],"form":[4,12,36,43,81,87],"linear":[5],"systems":[6,61],"is":[7,15,19],"considered":[8],"where":[9],"a":[10,46],"reduced":[13],"model":[14,37,91],"desired,":[16],"The":[17],"focus":[18],"on":[20,67],"methods":[22,72],"that":[23],"employ":[24],"or":[25],"mimic":[26],"Moore's":[27],"balance":[28,88],"and":[29,44,55,64,89],"truncate":[30,90],"(1981).":[31],"First,":[32],"we":[33],"examine":[34],"by":[39],"conversion":[40],"to":[41,78],"first-order":[42,86],"obtain":[45],"complete":[47],"solution":[48],"for":[49,59,83],"this":[50],"problem.":[51],"Then,":[52],"new":[53],"Gramians":[54],"input/output":[56],"(I/O)":[57],"invariants":[58],"are":[62,73,96],"motivated":[63],"defined.":[65],"Based":[66],"these,":[68],"direct":[69,79],"balancing":[71],"developed.":[74],"This":[75],"leads":[76],"naturally":[77],"analogs":[82],"the":[84,99],"well-known":[85],"method.":[93],"Explicit":[94],"algorithms":[95],"given":[97],"throughout":[98],"paper.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
