{"id":"https://openalex.org/W3121058966","doi":"https://doi.org/10.1109/cdc42340.2020.9304427","title":"A Continuation Method for computation of H<sub>\u221e</sub> gains of Linear Continuous-Time Periodic Systems","display_name":"A Continuation Method for computation of H<sub>\u221e</sub> gains of Linear Continuous-Time Periodic Systems","publication_year":2020,"publication_date":"2020-12-14","ids":{"openalex":"https://openalex.org/W3121058966","doi":"https://doi.org/10.1109/cdc42340.2020.9304427","mag":"3121058966"},"language":"en","primary_location":{"id":"doi:10.1109/cdc42340.2020.9304427","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9304427","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03213239","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065628882","display_name":"Paul Rousse","orcid":null},"institutions":[{"id":"https://openalex.org/I2801658355","display_name":"Office National d'\u00c9tudes et de Recherches A\u00e9rospatiales","ror":"https://ror.org/005y2ap84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2801658355"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Paul Rousse","raw_affiliation_strings":["ONERA, Toulouse, France"],"affiliations":[{"raw_affiliation_string":"ONERA, Toulouse, France","institution_ids":["https://openalex.org/I2801658355"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071811672","display_name":"John Hauser","orcid":"https://orcid.org/0000-0002-8129-7832"},"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":false,"raw_author_name":"John Hauser","raw_affiliation_strings":["University of Colorado Boulder, Boulder, CO, USA"],"affiliations":[{"raw_affiliation_string":"University of Colorado Boulder, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112600644","display_name":"P. Garoche","orcid":null},"institutions":[{"id":"https://openalex.org/I2801658355","display_name":"Office National d'\u00c9tudes et de Recherches A\u00e9rospatiales","ror":"https://ror.org/005y2ap84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2801658355"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre-Loic Garoche","raw_affiliation_strings":["ONERA, Toulouse, France"],"affiliations":[{"raw_affiliation_string":"ONERA, Toulouse, France","institution_ids":["https://openalex.org/I2801658355"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065628882"],"corresponding_institution_ids":["https://openalex.org/I2801658355"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24674115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":null,"first_page":"4653","last_page":"4658"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.7085261940956116},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6520964503288269},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5856022834777832},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5053258538246155},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4911913573741913},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.46240144968032837},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4601038694381714},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.458863228559494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4504009485244751},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4291335940361023},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.4281112849712372},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3713516592979431},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31440669298171997},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28733351826667786},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1946348249912262},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12167230248451233},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06628403067588806}],"concepts":[{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.7085261940956116},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6520964503288269},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5856022834777832},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5053258538246155},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4911913573741913},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.46240144968032837},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4601038694381714},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.458863228559494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4504009485244751},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4291335940361023},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.4281112849712372},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3713516592979431},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31440669298171997},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28733351826667786},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1946348249912262},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12167230248451233},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06628403067588806},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":3,"locations":[{"id":"doi:10.1109/cdc42340.2020.9304427","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9304427","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-03213239v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03213239","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":"2020 59th IEEE Conference on Decision and Control (CDC), Dec 2020, Jeju, South Korea. pp.4653-4658, &#x27E8;10.1109/CDC42340.2020.9304427&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/35794","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/35794","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Communication dans un congr\u00e8s avec actes"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03213239v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03213239","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":"2020 59th IEEE Conference on Decision and Control (CDC), Dec 2020, Jeju, South Korea. pp.4653-4658, &#x27E8;10.1109/CDC42340.2020.9304427&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1565627164","https://openalex.org/W1607862333","https://openalex.org/W1989312874","https://openalex.org/W1999484566","https://openalex.org/W2012604200","https://openalex.org/W2018496321","https://openalex.org/W2028791438","https://openalex.org/W2035354488","https://openalex.org/W2051112850","https://openalex.org/W2059527156","https://openalex.org/W2116462184","https://openalex.org/W2149175171","https://openalex.org/W2289990676","https://openalex.org/W2337289968","https://openalex.org/W2661232602","https://openalex.org/W4243644504","https://openalex.org/W4252130364","https://openalex.org/W6659146457","https://openalex.org/W6662931076","https://openalex.org/W6691373577","https://openalex.org/W6696485081","https://openalex.org/W6816008239"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2012352190","https://openalex.org/W4229560034","https://openalex.org/W4210910892","https://openalex.org/W2206497186","https://openalex.org/W4225691068","https://openalex.org/W4225895919"],"abstract_inverted_index":{"A":[0],"continuation":[1,102,116],"method":[2,103,117],"is":[3,66,128,155],"applied":[4],"to":[5,133,138,158],"compute":[6],"the":[7,53,64,84,87,101,105,134,153,159,162],"H":[8,19],"<sub":[9,20],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10,21],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e</sub>":[11,22],"gain":[12,23,46,62,85,126],"of":[13,24,45,100,161,164],"a":[14,25,35,60,67,80,108,115,123],"periodic":[15,26],"linear":[16,27],"system.":[17],"The":[18,125],"system":[28,163],"can":[29,55,74,89,118],"be":[30,56,75,90,119],"equivalently":[31],"found":[32],"by":[33,92],"solving":[34,93],"Periodic":[36,68],"Differential":[37,69],"Riccati":[38],"Equation":[39,71],"(PDRE)":[40],"for":[41,59,79,121,150],"an":[42,98],"increasing":[43],"sequence":[44],"candidates":[47],"until":[48,130],"no":[49,131],"solution":[50,88,132],"exists.":[51,136],"Solving":[52],"PDRE":[54,65,135],"cumbersome.":[57],"However,":[58],"null":[61],"candidate,":[63,86],"Lyapunov":[70],"(PDLE)":[72],"that":[73],"solved":[76],"efficiently.":[77],"Similarly,":[78],"small":[81],"increase":[82],"in":[83],"approximated":[91],"another":[94],"PDLE.":[95],"We":[96],"describe":[97],"application":[99],"where":[104,152],"corrector":[106],"uses":[107],"Boundary":[109],"Value":[110],"Problem":[111],"solver.":[112],"Therefore,":[113],"using":[114],"promising":[120],"such":[122],"problem.":[124],"candidate":[127],"increased":[129],"Compared":[137],"Hamiltonian":[139],"based":[140],"approaches,":[141],"our":[142],"approach":[143],"suffers":[144],"less":[145],"from":[146],"ill-conditioned":[147],"differential":[148],"equations":[149],"systems":[151],"periodicity":[154],"long":[156],"compared":[157],"dynamic":[160],"interest.":[165]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2021-01-18T00:00:00"}
