{"id":"https://openalex.org/W2789432567","doi":"https://doi.org/10.1109/tac.2018.2817163","title":"The Structured Distance to the Nearest System Without Property $\\mathcal {P}$","display_name":"The Structured Distance to the Nearest System Without Property $\\mathcal {P}$","publication_year":2018,"publication_date":"2018-03-19","ids":{"openalex":"https://openalex.org/W2789432567","doi":"https://doi.org/10.1109/tac.2018.2817163","mag":"2789432567"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2018.2817163","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2817163","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/A5101828179","display_name":"Scott C. Johnson","orcid":"https://orcid.org/0000-0001-6759-1659"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Scott C. Johnson","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040471364","display_name":"Mark Wicks","orcid":"https://orcid.org/0000-0002-0355-7782"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Wicks","raw_affiliation_strings":["Xometry, Bethesda, MD, USA"],"affiliations":[{"raw_affiliation_string":"Xometry, Bethesda, MD, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062331167","display_name":"Milo\u0161 \u017defran","orcid":"https://orcid.org/0000-0001-9558-3656"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Milos Zefran","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010068315","display_name":"Raymond A. DeCarlo","orcid":"https://orcid.org/0000-0003-3351-1563"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raymond A. DeCarlo","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101828179"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":1.1036,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.77791759,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"63","issue":"9","first_page":"2960","last_page":"2975"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9993000030517578,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.991100013256073,"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/mathematics","display_name":"Mathematics","score":0.7405054569244385},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.7148456573486328},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6214718222618103},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6193525791168213},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5640710592269897},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.5535498261451721},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34892845153808594},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3274992108345032},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.30763787031173706},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07339847087860107}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7405054569244385},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7148456573486328},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6214718222618103},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6193525791168213},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5640710592269897},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.5535498261451721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34892845153808594},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3274992108345032},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30763787031173706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07339847087860107},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2018.2817163","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2817163","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W66060913","https://openalex.org/W83533993","https://openalex.org/W121091459","https://openalex.org/W653924242","https://openalex.org/W1534416612","https://openalex.org/W1540740906","https://openalex.org/W1981482844","https://openalex.org/W2007954101","https://openalex.org/W2010082976","https://openalex.org/W2032200063","https://openalex.org/W2039579092","https://openalex.org/W2062209623","https://openalex.org/W2062710697","https://openalex.org/W2095590702","https://openalex.org/W2100486700","https://openalex.org/W2122883651","https://openalex.org/W2123353000","https://openalex.org/W2125152460","https://openalex.org/W2143987183","https://openalex.org/W2151177951","https://openalex.org/W2164349943","https://openalex.org/W2472587445","https://openalex.org/W2615378293","https://openalex.org/W2683103220","https://openalex.org/W2947553656","https://openalex.org/W6720807178","https://openalex.org/W6737778276"],"related_works":["https://openalex.org/W1986570998","https://openalex.org/W2332386680","https://openalex.org/W1983142522","https://openalex.org/W2782529250","https://openalex.org/W2508171592","https://openalex.org/W2037921533","https://openalex.org/W2801563517","https://openalex.org/W2130864543","https://openalex.org/W2068126039","https://openalex.org/W2041749520"],"abstract_inverted_index":{"For":[0],"a":[1,18,44,78,105,124],"system":[2,19],"matrix":[3,46,89,114],"M,":[4],"this":[5],"paper":[6],"explores":[7],"the":[8,33,66,72,116],"smallest":[9,37],"(Frobenius)":[10],"norm":[11,39,57,81,108],"additive":[12],"structured":[13,34,82,109],"perturbation":[14,35,73,84,110],"\u03b4M":[15,31,85],"for":[16,50],"which":[17,51],"property":[20,45,88,113],"P":[21,49],"(e.g.,":[22],"controllability,":[23],"observability,":[24],"stability,":[25],"etc.)":[26],"fails":[27],"to":[28],"hold,":[29],"i.e.,":[30],"is":[32,58,99,121],"with":[36],"Frobenius":[38,56],"such":[40],"that":[41,103],"there":[42],"exists":[43],"R":[47,90],"E":[48],"M-\u03b4M-R":[52],"drops":[53],"rank.":[54],"The":[55],"used":[59],"because":[60],"of":[61,68],"its":[62],"direct":[63],"dependence":[64],"on":[65,77],"magnitude":[67],"each":[69],"entry":[70],"in":[71],"matrix.":[74],"Necessary":[75],"conditions":[76],"locally":[79,106],"minimum":[80,107],"rank-reducing":[83],"and":[86,94,111],"associated":[87,112],"are":[91],"set":[92,101],"forth":[93,102],"proven.":[95],"An":[96],"iterative":[97],"algorithm":[98],"also":[100],"computes":[104],"satisfying":[115],"necessary":[117],"conditions.":[118],"Algorithm":[119],"convergence":[120],"proven":[122],"using":[123],"discrete":[125],"Lyapunov":[126],"function.":[127]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}