{"id":"https://openalex.org/W2529352710","doi":"https://doi.org/10.1137/16m1099467","title":"Infinite-Dimensional Input-to-State Stability and Orlicz Spaces","display_name":"Infinite-Dimensional Input-to-State Stability and Orlicz Spaces","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2529352710","doi":"https://doi.org/10.1137/16m1099467","mag":"2529352710"},"language":"en","primary_location":{"id":"doi:10.1137/16m1099467","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1099467","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1609.09741","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082176398","display_name":"Birgit Jacob","orcid":"https://orcid.org/0000-0002-8775-4424"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Birgit Jacob","raw_affiliation_strings":["Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany","Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany","School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039172004","display_name":"Robert Nabiullin","orcid":"https://orcid.org/0000-0002-7831-0426"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Robert Nabiullin","raw_affiliation_strings":["Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany","Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany","School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067107161","display_name":"J. R. Partington","orcid":"https://orcid.org/0000-0002-6738-3216"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Jonathan R. Partington","raw_affiliation_strings":["Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany","School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom","Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011609914","display_name":"Felix L. Schwenninger","orcid":"https://orcid.org/0000-0002-2030-6504"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Felix L. Schwenninger","raw_affiliation_strings":["Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany","School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom","Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2030-6504","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstra\u00dfe 55, D-20146 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds LS2 9JT, Yorkshire, United King-dom","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Functional analysis group, School of Mathematics and Natural Sciences, University of Wuppertal, D-42119 Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.8695,"has_fulltext":false,"cited_by_count":106,"citation_normalized_percentile":{"value":0.98930216,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"56","issue":"2","first_page":"868","last_page":"889"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9866999983787537,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9786999821662903,"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/mathematics","display_name":"Mathematics","score":0.9054301977157593},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6543444395065308},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5957943797111511},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5579737424850464},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.49380120635032654},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4882214367389679},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.481385737657547},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4484640061855316},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.434548944234848},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.42683878540992737},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3303319811820984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07984808087348938}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9054301977157593},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6543444395065308},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5957943797111511},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5579737424850464},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.49380120635032654},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4882214367389679},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.481385737657547},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4484640061855316},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.434548944234848},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.42683878540992737},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3303319811820984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07984808087348938},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1099467","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1099467","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:125700","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1609.09741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.09741","pdf_url":"https://arxiv.org/pdf/1609.09741","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1609.09741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.09741","pdf_url":"https://arxiv.org/pdf/1609.09741","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4459347039","display_name":null,"funder_award_id":"RE 2917/4-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G757735895","display_name":null,"funder_award_id":"JA 735/12-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1507247344","https://openalex.org/W1560380432","https://openalex.org/W1983296011","https://openalex.org/W2001542964","https://openalex.org/W2009162797","https://openalex.org/W2012554607","https://openalex.org/W2017493230","https://openalex.org/W2021190957","https://openalex.org/W2030958501","https://openalex.org/W2031736705","https://openalex.org/W2036896457","https://openalex.org/W2049892514","https://openalex.org/W2057820893","https://openalex.org/W2080209002","https://openalex.org/W2092180670","https://openalex.org/W2154904699","https://openalex.org/W2157222019","https://openalex.org/W2162750481","https://openalex.org/W2163313703","https://openalex.org/W2177424877","https://openalex.org/W2247036405","https://openalex.org/W2288506286","https://openalex.org/W2479300520","https://openalex.org/W2571220503","https://openalex.org/W2776041833","https://openalex.org/W2963030552","https://openalex.org/W2963115112","https://openalex.org/W3100624220","https://openalex.org/W3103042728"],"related_works":["https://openalex.org/W2135584473","https://openalex.org/W2964223869","https://openalex.org/W2792539140","https://openalex.org/W2005808740","https://openalex.org/W2295130398","https://openalex.org/W2064951085","https://openalex.org/W2626141450","https://openalex.org/W2810740133","https://openalex.org/W2064919237","https://openalex.org/W2122531814"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"the":[3,30,39,65],"relation":[4],"between":[5],"input-to-state":[6,10,45,53],"stability":[7,11,46,54,83],"and":[8],"integral":[9,44],"is":[12,27],"studied":[13],"for":[14,38],"linear":[15,63],"infinite-dimensional":[16],"systems":[17,78],"with":[18,55,79,85],"an":[19],"unbounded":[20],"control":[21],"operator.":[22],"Although":[23],"a":[24],"special":[25],"focus":[26],"laid":[28],"on":[29],"case":[31],"$L^{\\infty}$,":[32],"general":[33],"function":[34],"spaces":[35],"are":[36,89],"considered":[37],"inputs.":[40],"We":[41],"show":[42],"that":[43],"can":[47,67],"be":[48,69],"characterized":[49],"in":[50,71],"terms":[51,72],"of":[52,73],"respect":[56,86],"to":[57,87],"Orlicz":[58],"spaces.":[59],"Since":[60],"we":[61],"consider":[62],"systems,":[64],"results":[66],"also":[68],"formulated":[70],"admissibility.":[74],"For":[75],"parabolic":[76],"diagonal":[77],"scalar":[80],"inputs,":[81],"both":[82],"notions":[84],"$L^\\infty$":[88],"equivalent.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
