{"id":"https://openalex.org/W2940593839","doi":"https://doi.org/10.1109/cdc40024.2019.9030224","title":"A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs","display_name":"A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W2940593839","doi":"https://doi.org/10.1109/cdc40024.2019.9030224","mag":"2940593839"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9030224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030224","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1904.10091","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008140673","display_name":"Sachin Shivakumar","orcid":"https://orcid.org/0000-0003-1353-2834"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sachin Shivakumar","raw_affiliation_strings":["Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA","Arizona State University,Engineering of Matter, Transport and Energy,Tempe,AZ,USA,85298"],"affiliations":[{"raw_affiliation_string":"Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University,Engineering of Matter, Transport and Energy,Tempe,AZ,USA,85298","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013924360","display_name":"Amritam Das","orcid":"https://orcid.org/0000-0001-8494-8509"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Amritam Das","raw_affiliation_strings":["Department of Electrical Engineering, Eindhoven University of Technology, MB, The Netherlands","Eindhoven University of Technology,Department of Electrical Engineering,MB,The Netherlands,5600"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Eindhoven University of Technology, MB, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Eindhoven University of Technology,Department of Electrical Engineering,MB,The Netherlands,5600","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006584942","display_name":"S. Weiland","orcid":"https://orcid.org/0000-0002-6131-4658"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Siep Weiland","raw_affiliation_strings":["Department of Electrical Engineering, Eindhoven University of Technology, MB, The Netherlands","Eindhoven University of Technology,Department of Electrical Engineering,MB,The Netherlands,5600"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Eindhoven University of Technology, MB, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Eindhoven University of Technology,Department of Electrical Engineering,MB,The Netherlands,5600","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077552862","display_name":"Matthew M. Peet","orcid":"https://orcid.org/0000-0001-9360-6738"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew M. Peet","raw_affiliation_strings":["Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA","Arizona State University,Engineering of Matter, Transport and Energy,Tempe,AZ,USA,85298"],"affiliations":[{"raw_affiliation_string":"Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University,Engineering of Matter, Transport and Energy,Tempe,AZ,USA,85298","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5008140673"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":1.623,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.81618497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"280","last_page":"285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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":0.9994999766349792,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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":0.7691992521286011},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7216305732727051},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.623252809047699},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5863921642303467},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5218302607536316},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5207069516181946},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5153355002403259},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4982149600982666},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4340163767337799},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4244352877140045},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3296127915382385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09620332717895508}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7691992521286011},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7216305732727051},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.623252809047699},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5863921642303467},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5218302607536316},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5207069516181946},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5153355002403259},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4982149600982666},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4340163767337799},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4244352877140045},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3296127915382385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09620332717895508},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/cdc40024.2019.9030224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030224","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.tue.nl:publications/5caa0c5f-d282-4e69-9dd9-0e50bcc7cfc9","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/5caa0c5f-d282-4e69-9dd9-0e50bcc7cfc9","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Shivakumar, S, Das, A, Weiland, S & Peet, M 2020, A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs. in 2019 IEEE 58th Conference on Decision and Control (CDC)., 9030224, pp. 280-285, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 11/12/19. https://doi.org/10.1109/CDC40024.2019.9030224","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1904.10091","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.10091","pdf_url":"https://arxiv.org/pdf/1904.10091","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2940593839","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1904.10091v2","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:tue:oai:pure.tue.nl:publications/5caa0c5f-d282-4e69-9dd9-0e50bcc7cfc9","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/5caa0c5f-d282-4e69-9dd9-0e50bcc7cfc9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC), 280 - 285","raw_type":"info:eu-repo/semantics/conferencepaper"},{"id":"doi:10.48550/arxiv.1904.10091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.10091","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1904.10091","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.10091","pdf_url":"https://arxiv.org/pdf/1904.10091","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2940593839.pdf","grobid_xml":"https://content.openalex.org/works/W2940593839.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1971189895","https://openalex.org/W1972806290","https://openalex.org/W2005630198","https://openalex.org/W2012226489","https://openalex.org/W2015058232","https://openalex.org/W2022230833","https://openalex.org/W2058945808","https://openalex.org/W2080430932","https://openalex.org/W2106850246","https://openalex.org/W2119423238","https://openalex.org/W2169621160","https://openalex.org/W2199293409","https://openalex.org/W2273822880","https://openalex.org/W2529757039","https://openalex.org/W2556353703","https://openalex.org/W2808762422","https://openalex.org/W2905274485","https://openalex.org/W2913864289","https://openalex.org/W2963286893","https://openalex.org/W2963599370","https://openalex.org/W2969717913","https://openalex.org/W2973138143","https://openalex.org/W3102398605","https://openalex.org/W6684859714","https://openalex.org/W6752262576","https://openalex.org/W6757518609"],"related_works":["https://openalex.org/W3011946205","https://openalex.org/W2973138143","https://openalex.org/W2903862549","https://openalex.org/W2913864289","https://openalex.org/W2796192311","https://openalex.org/W3199529518","https://openalex.org/W2806643835","https://openalex.org/W2793310183","https://openalex.org/W3011283411","https://openalex.org/W3097480145","https://openalex.org/W1968775057","https://openalex.org/W2784412233","https://openalex.org/W2292830339","https://openalex.org/W2766044590","https://openalex.org/W3036397324","https://openalex.org/W2043092713","https://openalex.org/W1553335074","https://openalex.org/W2125901041","https://openalex.org/W2888368722","https://openalex.org/W2765128097"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"consider":[4],"input-output":[5],"properties":[6],"of":[7,11,24,33,48,58,69,79,92,140],"linear":[8],"systems":[9,42],"consisting":[10],"PDEs":[12],"on":[13],"a":[14,44,65,74],"finite":[15],"domain":[16],"coupled":[17,40],"with":[18,113],"ODEs":[19,38],"through":[20],"the":[21,25,30,34,52,59,77,93,110],"boundary":[22],"conditions":[23,57],"PDE.":[26],"This":[27],"work":[28],"generalizes":[29],"sufficiency":[31],"proof":[32],"KYP":[35,61],"Lemma":[36],"for":[37],"to":[39],"ODE-PDE":[41],"using":[43,64],"recently":[45],"developed":[46],"concept":[47],"fundamental":[49],"state":[50],"and":[51,104,128],"associated":[53],"boundary-condition-free":[54],"representation.":[55],"The":[56],"generalized":[60],"are":[62,121],"tested":[63],"positive":[66],"matrix":[67],"parameterization":[68],"bounded":[70],"operators":[71],"resulting":[72],"in":[73,109,124],"finite-dimensional":[75,138],"LMI,":[76],"feasibility":[78],"which":[80],"implies":[81],"prima":[82],"facie":[83],"provable":[84],"passivity":[85],"or":[86,97],"L":[87],"<sub":[88],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[89],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[90],"-gain":[91],"system.":[94],"No":[95],"discretization":[96],"approximation":[98],"is":[99,106,132],"involved":[100],"at":[101],"any":[102,125],"step":[103],"there":[105],"no":[107],"conservatism":[108],"theorems.":[111],"Comparison":[112],"other":[114],"computational":[115,130],"methods":[116,136],"show":[117],"that":[118,129],"bounds":[119],"obtained":[120],"not":[122],"conservative":[123],"significant":[126],"sense":[127],"complexity":[131],"lower":[133],"than":[134],"existing":[135],"involving":[137],"projection":[139],"PDEs.":[141]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}