{"id":"https://openalex.org/W2154695653","doi":"https://doi.org/10.1109/cdc.2009.5400093","title":"Stability and stabilization of a class of ill-conditioned second order differential linear repetitive processes","display_name":"Stability and stabilization of a class of ill-conditioned second order differential linear repetitive processes","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2154695653","doi":"https://doi.org/10.1109/cdc.2009.5400093","mag":"2154695653"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2009.5400093","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400093","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese 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/A5015555379","display_name":"Pawe\u0142 D\u0105bkowski","orcid":"https://orcid.org/0000-0003-2751-8486"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Pawel Dabkowski","raw_affiliation_strings":["Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Poland","institution_ids":["https://openalex.org/I3019271933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066492464","display_name":"Krzysztof Ga\u0142kowski","orcid":"https://orcid.org/0000-0003-4470-2162"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Galkowski","raw_affiliation_strings":["Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Poland","institution_ids":["https://openalex.org/I3019271933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081788754","display_name":"Eric Rogers","orcid":"https://orcid.org/0000-0003-0179-9398"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Eric Rogers","raw_affiliation_strings":["School of Electronics and Computer Science, University of Southampton, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronics and Computer Science, University of Southampton, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"230","issue":null,"first_page":"3232","last_page":"3237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11749","display_name":"Iterative Learning Control Systems","score":0.9997000098228455,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9997000098228455,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9835000038146973,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9815000295639038,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6562607884407043},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5896468758583069},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.552142858505249},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4962378144264221},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.479369193315506},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.47843673825263977},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.45149701833724976},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4497326910495758},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.44511258602142334},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44124525785446167},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.4305822253227234},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.41595423221588135},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3411508798599243},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2107710838317871},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18878650665283203},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11850708723068237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11283662915229797}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6562607884407043},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5896468758583069},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.552142858505249},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4962378144264221},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.479369193315506},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.47843673825263977},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.45149701833724976},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4497326910495758},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.44511258602142334},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44124525785446167},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.4305822253227234},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.41595423221588135},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3411508798599243},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2107710838317871},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18878650665283203},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11850708723068237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11283662915229797},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2009.5400093","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400093","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W67671487","https://openalex.org/W130632564","https://openalex.org/W640910350","https://openalex.org/W1536312024","https://openalex.org/W1538439529","https://openalex.org/W1964594672","https://openalex.org/W1989099401","https://openalex.org/W2010516768","https://openalex.org/W2049719597","https://openalex.org/W2076426180","https://openalex.org/W2140440476","https://openalex.org/W2154443534","https://openalex.org/W2166728224","https://openalex.org/W2200810213","https://openalex.org/W2616582517","https://openalex.org/W4246404290","https://openalex.org/W4392147440","https://openalex.org/W6632319148","https://openalex.org/W6682144463","https://openalex.org/W6687395271"],"related_works":["https://openalex.org/W2164889171","https://openalex.org/W1859237763","https://openalex.org/W2394154139","https://openalex.org/W2011061487","https://openalex.org/W2368658599","https://openalex.org/W2363168083","https://openalex.org/W2381464044","https://openalex.org/W4385498498","https://openalex.org/W2351140947","https://openalex.org/W2358829338"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"differential":[3,49],"linear":[4,50,130],"repetitive":[5],"processes":[6,58,69],"which":[7],"are":[8],"a":[9,19,40,47,60,118],"distinct":[10],"class":[11],"of":[12,21,26,75,116],"2D":[13,28],"systems":[14],"whose":[15],"dynamics":[16],"evolve":[17],"over":[18,39],"subset":[20],"the":[22,27,72,76,81,102,114],"upper":[23],"right":[24],"quadrant":[25],"plane.":[29],"In":[30],"particular,":[31],"information":[32],"propagation":[33],"in":[34,63,80],"one":[35],"direction":[36],"only":[37],"occurs":[38],"finite":[41],"duration":[42],"and":[43,92],"is":[44],"governed":[45],"by":[46,99],"matrix":[48,79,131],"equation.":[51],"A":[52],"stability":[53,90],"theory":[54],"exists":[55],"for":[56,96],"these":[57],"but":[59],"problem":[61],"arises":[62],"its":[64],"application":[65],"to":[66,71,106],"second":[67],"order":[68],"due":[70],"possible":[73],"ill-conditioning":[74],"leading":[77],"coefficient":[78],"state-space":[82,104],"model.":[83],"Here":[84],"we":[85],"derive":[86],"new":[87],"results":[88,123],"on":[89],"analysis":[91],"control":[93],"law":[94],"design":[95],"this":[97],"case":[98],"first":[100],"transforming":[101],"second-order":[103],"model":[105],"an":[107],"equivalent":[108],"first-order":[109],"descriptor":[110],"system,":[111],"thus":[112],"avoiding":[113],"necessity":[115],"inverting":[117],"possibly":[119],"ill-conditioned":[120],"matrix.":[121],"The":[122],"developed":[124],"here":[125],"can":[126],"be":[127],"computed":[128],"using":[129],"inequalities":[132],"(LMIs).":[133]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
