{"id":"https://openalex.org/W4387245215","doi":"https://doi.org/10.1109/tac.2023.3321236","title":"Convergence of Nonlinear Observers on With a Riemannian Metric (Part III)","display_name":"Convergence of Nonlinear Observers on With a Riemannian Metric (Part III)","publication_year":2023,"publication_date":"2023-10-02","ids":{"openalex":"https://openalex.org/W4387245215","doi":"https://doi.org/10.1109/tac.2023.3321236"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2023.3321236","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tac.2023.3321236","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/A5028224738","display_name":"Ricardo G. Sanfelice","orcid":"https://orcid.org/0000-0002-6671-5362"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ricardo G. Sanfelice","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-6671-5362","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, USA","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101466166","display_name":"Laurent Praly","orcid":"https://orcid.org/0000-0003-4380-7616"},"institutions":[{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurent Praly","raw_affiliation_strings":["CAS, ParisTech, Ecole des Mines, Fontainebleau, France"],"raw_orcid":"https://orcid.org/0000-0003-4380-7616","affiliations":[{"raw_affiliation_string":"CAS, ParisTech, Ecole des Mines, Fontainebleau, France","institution_ids":["https://openalex.org/I70768539"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1636,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45857559,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"69","issue":"3","first_page":"1432","last_page":"1447"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9927999973297119,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9927999973297119,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9922999739646912,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.974399983882904,"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/geodesic","display_name":"Geodesic","score":0.7589631080627441},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7014786601066589},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6507833003997803},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5892220139503479},{"id":"https://openalex.org/keywords/fundamental-theorem-of-riemannian-geometry","display_name":"Fundamental theorem of Riemannian geometry","score":0.5282993316650391},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5269609093666077},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5086158514022827},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5069589614868164},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4903526306152344},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.47905075550079346},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4537102282047272},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.4448365569114685},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42879506945610046},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4069153666496277},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.13750767707824707},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09993213415145874}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7589631080627441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7014786601066589},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6507833003997803},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5892220139503479},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.5282993316650391},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5269609093666077},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5086158514022827},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5069589614868164},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4903526306152344},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.47905075550079346},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4537102282047272},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4448365569114685},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42879506945610046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4069153666496277},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.13750767707824707},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09993213415145874},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2023.3321236","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tac.2023.3321236","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":[{"id":"https://openalex.org/G2574428355","display_name":null,"funder_award_id":"FA8651-22-1-0017","funder_id":"https://openalex.org/F4320338294","funder_display_name":"Air Force Research Laboratory"},{"id":"https://openalex.org/G5932844992","display_name":null,"funder_award_id":"FA8651-23-1-0004","funder_id":"https://openalex.org/F4320338294","funder_display_name":"Air Force Research Laboratory"},{"id":"https://openalex.org/G6191118875","display_name":null,"funder_award_id":"FA9550-19-1-0169","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7107794925","display_name":null,"funder_award_id":"FA9550-20-1-0238","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7780225566","display_name":null,"funder_award_id":"FA9550-23-1-0145","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7801961505","display_name":null,"funder_award_id":"FA9550-23-1-0313","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338294","display_name":"Air Force Research Laboratory","ror":"https://ror.org/02e2egq70"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W90133503","https://openalex.org/W130251911","https://openalex.org/W174034496","https://openalex.org/W597303087","https://openalex.org/W658193902","https://openalex.org/W1518981959","https://openalex.org/W1557324374","https://openalex.org/W1559840026","https://openalex.org/W1587069887","https://openalex.org/W1974228548","https://openalex.org/W2000505041","https://openalex.org/W2007556045","https://openalex.org/W2009664999","https://openalex.org/W2019041168","https://openalex.org/W2063157339","https://openalex.org/W2083402998","https://openalex.org/W2090048018","https://openalex.org/W2097089521","https://openalex.org/W2103095193","https://openalex.org/W2104068117","https://openalex.org/W2106805668","https://openalex.org/W2114136077","https://openalex.org/W2128765522","https://openalex.org/W2140214428","https://openalex.org/W2160821152","https://openalex.org/W2320012146","https://openalex.org/W2320116016","https://openalex.org/W2587774887","https://openalex.org/W2616155687","https://openalex.org/W2896405912","https://openalex.org/W3103348869","https://openalex.org/W4246883249","https://openalex.org/W6607088748"],"related_works":["https://openalex.org/W4291625303","https://openalex.org/W3103229299","https://openalex.org/W1976330683","https://openalex.org/W3183653752","https://openalex.org/W2737579912","https://openalex.org/W1486814401","https://openalex.org/W4293874102","https://openalex.org/W4245686311","https://openalex.org/W1999110602","https://openalex.org/W2952578374"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2],"the":[3,19,22,39,43,60,64,75,81,84,89,109],"third":[4],"and":[5,24,42,54,95,108,114],"final":[6],"component":[7],"of":[8,21,66,83,88],"a":[9,15,34,50,55,104,117,122],"three-part":[10],"effort":[11],"on":[12],"observers":[13],"contracting":[14],"Riemannian":[16,44],"distance":[17],"between":[18,106],"state":[20],"system":[23,40],"its":[25],"estimate.":[26],"In":[27],"Part":[28,67,71],"I,":[29],"we":[30,73,115,128],"showed":[31],"that":[32],"such":[33],"contraction":[35],"property":[36,53],"holds":[37],"if":[38],"dynamics":[41],"metric":[45,123],"satisfy":[46],"two":[47],"key":[48],"conditions:":[49],"differential":[51],"detectability":[52],"geodesic":[56],"monotonicity":[57],"property.":[58],"With":[59],"former":[61],"condition":[62,77],"being":[63],"focus":[65],"II,":[68],"in":[69,78],"this":[70,125],"III,":[72],"study":[74],"latter":[76],"relationship":[79],"to":[80,100],"nullity":[82],"second":[85],"fundamental":[86],"form":[87],"output":[90],"function.":[91],"We":[92,102],"formulate":[93],"sufficient":[94],"necessary":[96],"conditions":[97,133],"for":[98,120],"it":[99,107],"hold.":[101,134],"establish":[103],"link":[105],"infinite":[110],"gain":[111],"margin":[112],"property,":[113],"provide":[116],"systematic":[118],"way":[119],"constructing":[121],"satisfying":[124],"condition.":[126],"Finally,":[127],"illustrate":[129],"cases":[130],"where":[131],"both":[132]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}
