{"id":"https://openalex.org/W2135229502","doi":"https://doi.org/10.1109/acc.2007.4282408","title":"Non-smooth techniques for stabilizing linear systems","display_name":"Non-smooth techniques for stabilizing linear systems","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2135229502","doi":"https://doi.org/10.1109/acc.2007.4282408","mag":"2135229502"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282408","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282408","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5062242577","display_name":"Vincent Bompart","orcid":null},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I4210098964","display_name":"Toulouse Mathematics Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210098964"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Bompart","raw_affiliation_strings":["Institut de Math\u00e9matiques, ONERA-CERT, and Universit\u00e9 Paul Sabatier, Toulouse, France","Univ. Paul Sabatier, Toulouse"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques, ONERA-CERT, and Universit\u00e9 Paul Sabatier, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210098964"]},{"raw_affiliation_string":"Univ. Paul Sabatier, Toulouse","institution_ids":["https://openalex.org/I134560555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033569810","display_name":"Pierre Apkarian","orcid":"https://orcid.org/0000-0003-1122-9153"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I4210098964","display_name":"Toulouse Mathematics Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210098964"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Apkarian","raw_affiliation_strings":["Institut de Math\u00e9matiques, ONERA-CERT, and Universit\u00e9 Paul Sabatier, Toulouse, France","Univ. Paul Sabatier, Toulouse"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques, ONERA-CERT, and Universit\u00e9 Paul Sabatier, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210098964"]},{"raw_affiliation_string":"Univ. Paul Sabatier, Toulouse","institution_ids":["https://openalex.org/I134560555"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030567369","display_name":"Dominikus Noll","orcid":"https://orcid.org/0000-0002-8638-2438"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210092408","https://openalex.org/I4210126056","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominikus Noll","raw_affiliation_strings":["Institut de Math\u00e9matiques, Toulouse, France","Univ. Paul Sabatier, Toulouse"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques, Toulouse, France","institution_ids":["https://openalex.org/I84500057"]},{"raw_affiliation_string":"Univ. Paul Sabatier, Toulouse","institution_ids":["https://openalex.org/I134560555"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7214,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.97121685,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1245","last_page":"1250"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T11236","display_name":"Control Systems and Identification","score":0.9994999766349792,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9984999895095825,"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/maxima-and-minima","display_name":"Maxima and minima","score":0.6861739158630371},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5557888746261597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5446634888648987},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5395729541778564},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5202547311782837},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47881895303726196},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4456155300140381},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42090198397636414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33906424045562744},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23975658416748047},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16807299852371216},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10709407925605774}],"concepts":[{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.6861739158630371},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5557888746261597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5446634888648987},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5395729541778564},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5202547311782837},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47881895303726196},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4456155300140381},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42090198397636414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33906424045562744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23975658416748047},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16807299852371216},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10709407925605774},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2007.4282408","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282408","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.6431","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.6431","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mip.ups-tlse.fr/~noll/PAPERS/specabs.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1536758725","https://openalex.org/W1537335979","https://openalex.org/W1551360398","https://openalex.org/W1553702074","https://openalex.org/W1981188096","https://openalex.org/W2012604200","https://openalex.org/W2021073573","https://openalex.org/W2036881208","https://openalex.org/W2038648531","https://openalex.org/W2039606278","https://openalex.org/W2042844238","https://openalex.org/W2048922416","https://openalex.org/W2057366835","https://openalex.org/W2064558818","https://openalex.org/W2064942524","https://openalex.org/W2075341894","https://openalex.org/W2079688774","https://openalex.org/W2081989804","https://openalex.org/W2094507464","https://openalex.org/W2100210445","https://openalex.org/W2112704952","https://openalex.org/W2115955567","https://openalex.org/W2117649194","https://openalex.org/W2120267268","https://openalex.org/W2147228817","https://openalex.org/W2178909929","https://openalex.org/W2180470641","https://openalex.org/W2284696297","https://openalex.org/W2612868624","https://openalex.org/W2764109323","https://openalex.org/W4246146048","https://openalex.org/W4247489173","https://openalex.org/W6632629376","https://openalex.org/W6645519702","https://openalex.org/W6659942040","https://openalex.org/W6671318683","https://openalex.org/W6695910987","https://openalex.org/W6827570460"],"related_works":["https://openalex.org/W2375684291","https://openalex.org/W2354676191","https://openalex.org/W3188646203","https://openalex.org/W2909957174","https://openalex.org/W136674370","https://openalex.org/W4246278799","https://openalex.org/W2105527480","https://openalex.org/W2052387497","https://openalex.org/W2050203848","https://openalex.org/W2050191802"],"abstract_inverted_index":{"We":[0],"discuss":[1],"closed-loop":[2,70],"stabilization":[3,32],"of":[4,68,77,91],"linear":[5],"time-invariant":[6],"dynamical":[7],"systems,":[8],"a":[9,19,149],"problem":[10],"which":[11],"frequently":[12],"arises":[13],"in":[14],"controller":[15],"synthesis,":[16],"either":[17],"as":[18,148],"stand-alone":[20],"task,":[21],"or":[22,28,37],"to":[23,41,63,83,112,116,119,131],"initialize":[24],"algorithms":[25],"for":[26,44,105],"Hinfinsynthesis":[27],"related":[29],"problems.":[30],"Classical":[31],"methods":[33,50,81,138],"based":[34],"on":[35],"Lyapunov":[36],"Riccati":[38],"equations":[39],"appear":[40],"be":[42],"inefficient":[43],"large":[45],"systems.":[46],"Recently,":[47],"non-smooth":[48,86,103],"optimization":[49],"like":[51],"gradient":[52],"sampling":[53],"[J.V.":[54],"Burke":[55],"et":[56],"al.,":[57],"2002]":[58],"have":[59,82],"been":[60],"successfully":[61],"used":[62],"minimize":[64],"the":[65,69,85,92,110,126,143],"spectral":[66,93,144],"abscissa":[67,94,145],"state":[71],"matrix":[72],"(the":[73],"largest":[74],"real":[75],"part":[76],"its":[78],"eigenvalues).":[79],"These":[80],"address":[84],"and":[87,139],"even":[88],"non-Lipschitz":[89],"character":[90],"function.":[95],"In":[96],"this":[97],"work,":[98],"we":[99],"develop":[100],"an":[101],"alternative":[102],"technique":[104,128],"solving":[106],"similar":[107],"problems,":[108],"with":[109],"option":[111],"incorporate":[113],"second-order":[114],"elements":[115],"speed-up":[117],"convergence":[118],"local":[120],"minima.":[121],"Using":[122],"several":[123],"case":[124],"studies,":[125],"proposed":[127],"is":[129,146],"compared":[130],"more":[132],"conventional":[133],"approaches":[134],"including":[135],"direct":[136],"search":[137],"techniques":[140],"where":[141],"minimizing":[142],"recast":[147],"traditional":[150],"smooth":[151],"non-linear":[152],"mathematical":[153],"programming":[154],"problem.":[155]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
