{"id":"https://openalex.org/W3198932099","doi":"https://doi.org/10.1109/tcns.2021.3113263","title":"Functions of the Laplacian Matrix With Application to Distributed Formation Control","display_name":"Functions of the Laplacian Matrix With Application to Distributed Formation Control","publication_year":2021,"publication_date":"2021-09-16","ids":{"openalex":"https://openalex.org/W3198932099","doi":"https://doi.org/10.1109/tcns.2021.3113263","mag":"3198932099"},"language":"en","primary_location":{"id":"doi:10.1109/tcns.2021.3113263","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2021.3113263","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03710366","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026787189","display_name":"Fabio Morbidi","orcid":"https://orcid.org/0000-0002-7187-3410"},"institutions":[{"id":"https://openalex.org/I4647051","display_name":"Universit\u00e9 de Picardie Jules Verne","ror":"https://ror.org/01gyxrk03","country_code":"FR","type":"education","lineage":["https://openalex.org/I4647051"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fabio Morbidi","raw_affiliation_strings":["Modeling, Information and Systems Laboratory, Universit&#x00E9; de Picardie Jules Verne, Amiens, France"],"raw_orcid":"https://orcid.org/0000-0002-7187-3410","affiliations":[{"raw_affiliation_string":"Modeling, Information and Systems Laboratory, Universit&#x00E9; de Picardie Jules Verne, Amiens, France","institution_ids":["https://openalex.org/I4647051"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026787189"],"corresponding_institution_ids":["https://openalex.org/I4647051"],"apc_list":null,"apc_paid":null,"fwci":0.4558,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65633839,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"3","first_page":"1459","last_page":"1467"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9973000288009644,"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/laplacian-matrix","display_name":"Laplacian matrix","score":0.6846082210540771},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6690130829811096},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5516440272331238},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5477972030639648},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.5204418301582336},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.5077763199806213},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47213417291641235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4404003918170929},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41621583700180054},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.41533786058425903},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37903398275375366},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3424321413040161},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.3395390510559082},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19362595677375793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12741714715957642},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0830819308757782}],"concepts":[{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6846082210540771},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6690130829811096},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5516440272331238},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5477972030639648},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.5204418301582336},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.5077763199806213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47213417291641235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4404003918170929},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41621583700180054},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.41533786058425903},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37903398275375366},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3424321413040161},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3395390510559082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19362595677375793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12741714715957642},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0830819308757782},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcns.2021.3113263","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2021.3113263","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network Systems","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03710366v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03710366","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Control of Network Systems, 2022, 9 (3), pp.1459-1467. &#x27E8;10.1109/TCNS.2021.3113263&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03710366v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03710366","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Control of Network Systems, 2022, 9 (3), pp.1459-1467. &#x27E8;10.1109/TCNS.2021.3113263&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W613360614","https://openalex.org/W1483804921","https://openalex.org/W1499071767","https://openalex.org/W1527992869","https://openalex.org/W1551112541","https://openalex.org/W2003684104","https://openalex.org/W2016423476","https://openalex.org/W2029443449","https://openalex.org/W2029616478","https://openalex.org/W2039410288","https://openalex.org/W2096146461","https://openalex.org/W2099700272","https://openalex.org/W2114990297","https://openalex.org/W2136935487","https://openalex.org/W2168914013","https://openalex.org/W2442203778","https://openalex.org/W2460760569","https://openalex.org/W2497633600","https://openalex.org/W2601954554","https://openalex.org/W2616297073","https://openalex.org/W2758203196","https://openalex.org/W2796431263","https://openalex.org/W2907492528","https://openalex.org/W2921089641","https://openalex.org/W2927197384","https://openalex.org/W2936525257","https://openalex.org/W2944101636","https://openalex.org/W2962759781","https://openalex.org/W2963084622","https://openalex.org/W2982546823","https://openalex.org/W2995201243","https://openalex.org/W3010591705","https://openalex.org/W3086411969","https://openalex.org/W3095521706","https://openalex.org/W3103510559","https://openalex.org/W3122996080","https://openalex.org/W4235019172","https://openalex.org/W4238591275","https://openalex.org/W4240790602","https://openalex.org/W6679406828","https://openalex.org/W6762785561","https://openalex.org/W6990345839"],"related_works":["https://openalex.org/W1529195008","https://openalex.org/W2070323717","https://openalex.org/W2570009360","https://openalex.org/W3157489721","https://openalex.org/W3004345458","https://openalex.org/W2883186538","https://openalex.org/W38983538","https://openalex.org/W2924468784","https://openalex.org/W2051180862","https://openalex.org/W2748456403"],"abstract_inverted_index":{"In":[0],"this":[1,64],"article,":[2],"we":[3,62,73],"study":[4],"a":[5,55,109],"class":[6],"of":[7,10,40,44,66,88],"matrix":[8,47],"functions":[9,68,107],"the":[11,38,45,59,78],"combinatorial":[12],"Laplacian":[13,46,67,106],"that":[14,19,48,75],"preserve":[15],"its":[16],"structure,":[17],"i.e.,":[18],"define":[20],"matrices,":[21],"which":[22,27],"are":[23],"positive":[24],"semidefinite":[25],"and":[26,31,72,82,90,100],"have":[28,49],"zero":[29],"row-sum":[30],"nonpositive":[32],"off-diagonal":[33],"entries.":[34],"This":[35],"formulation":[36],"has":[37],"merit":[39],"presenting":[41],"different":[42],"incarnations":[43],"appeared":[50],"in":[51,54,86,108],"recent":[52],"literature":[53],"unified":[56],"framework.":[57],"For":[58],"first":[60],"time,":[61],"apply":[63],"family":[65],"to":[69],"consensus":[70],"theory,":[71],"show":[74],"they":[76],"leave":[77],"agreement":[79],"value":[80],"unchanged":[81],"offer":[83],"distinctive":[84],"advantages":[85],"terms":[87],"performance":[89],"design":[91],"flexibility.":[92],"The":[93],"theory":[94],"is":[95],"illustrated":[96],"via":[97],"worked":[98],"examples":[99],"numerical":[101],"experiments":[102],"featuring":[103],"four":[104],"representative":[105],"shape-based":[110],"distributed":[111],"formation":[112],"control":[113],"strategy":[114],"for":[115],"single-integrator":[116],"robots.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
