{"id":"https://openalex.org/W2135311228","doi":"https://doi.org/10.1109/cdc.2003.1272880","title":"A classification of all solutions of the algebraic Riccati equations for infinite-dimensional systems","display_name":"A classification of all solutions of the algebraic Riccati equations for infinite-dimensional systems","publication_year":2004,"publication_date":"2004-07-08","ids":{"openalex":"https://openalex.org/W2135311228","doi":"https://doi.org/10.1109/cdc.2003.1272880","mag":"2135311228"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2003.1272880","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1272880","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","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/A5025340972","display_name":"Orest Iftime","orcid":"https://orcid.org/0000-0002-2867-9524"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"O. Iftime","raw_affiliation_strings":["Mathematics Institute, University of Groningen, Groningen, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Groningen, Groningen, Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109132221","display_name":"Ruth F. Curtain","orcid":null},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"R. Curtain","raw_affiliation_strings":["Mathematics Institute, University of Groningen, Groningen, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Groningen, Groningen, Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041102285","display_name":"Hans Zwart","orcid":"https://orcid.org/0000-0003-3451-7967"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]},{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H. Zwart","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Netherlands","Mathematics Institute, University of Groningam, Groningen, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Netherlands","institution_ids":["https://openalex.org/I94624287"]},{"raw_affiliation_string":"Mathematics Institute, University of Groningam, Groningen, Netherlands","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"1836","last_page":"1841"},"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":0.9980000257492065,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9977999925613403,"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/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.9442224502563477},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8448030948638916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6999953389167786},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6848748326301575},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6621308922767639},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.6162287592887878},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5383322238922119},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5043007135391235},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.41675910353660583},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39450299739837646},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.39432692527770996},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3548211455345154},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34155356884002686},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31471532583236694},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16793930530548096},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16060012578964233},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1602187156677246},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06832018494606018}],"concepts":[{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.9442224502563477},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8448030948638916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6999953389167786},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6848748326301575},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6621308922767639},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.6162287592887878},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5383322238922119},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5043007135391235},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.41675910353660583},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39450299739837646},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.39432692527770996},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3548211455345154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34155356884002686},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31471532583236694},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16793930530548096},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16060012578964233},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1602187156677246},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06832018494606018},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cdc.2003.1272880","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1272880","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","raw_type":"proceedings-article"},{"id":"pmh:oai:ris.utwente.nl:openaire_cris_publications/9addf63f-6c28-4a59-b725-046ee58ee425","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/9addf63f-6c28-4a59-b725-046ee58ee425","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":"Iftime, O, Curtain, R & Zwart, H 2003, A classification of all solutions of the Algebraic Riccati Equations for Infinite-Dimensional systems. in 42nd IEEE International Conference on Decision and Control 2003. vol. 2, IEEE Conference on Decision and Control, vol. 2003, IEEE, Piscataway, NJ, pp. 1836-1841, 42nd IEEE Conference on Decision and Control, CDC 2003, Maui, Hawaii, United States, 9/12/03. https://doi.org/10.1109/CDC.2003.1272880","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:pure.rug.nl:publications/879cf57d-34f6-44e6-954a-84a0ac90466f","is_oa":false,"landing_page_url":"https://hdl.handle.net/11370/879cf57d-34f6-44e6-954a-84a0ac90466f","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Iftime, O, Curtain, R & Zwart, H 2003, Classification of all solutions of the algebraic Riccati equations for infinite-dimensional systems. in 42ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-6, PROCEEDINGS. IEEE (The Institute of Electrical and Electronics Engineers), NEW YORK, pp. 1836-1841, 42nd IEEE Conference on Decision and Control, 09/12/2003.","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:rug:oai:pure.rug.nl:publications/879cf57d-34f6-44e6-954a-84a0ac90466f","is_oa":false,"landing_page_url":"https://research.rug.nl/en/publications/879cf57d-34f6-44e6-954a-84a0ac90466f","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":"42ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-6, PROCEEDINGS, 1836 - 1841","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W197984925","https://openalex.org/W1036056737","https://openalex.org/W1538686203","https://openalex.org/W1929958170","https://openalex.org/W1968350782","https://openalex.org/W1990525542","https://openalex.org/W2002357820","https://openalex.org/W2004307586","https://openalex.org/W2022968366","https://openalex.org/W2041513795","https://openalex.org/W2042106612","https://openalex.org/W2048949483","https://openalex.org/W2091634205","https://openalex.org/W2097327029","https://openalex.org/W2173130135"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2727200542","https://openalex.org/W2002357820","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2027962246","https://openalex.org/W2804494800","https://openalex.org/W2116228702"],"abstract_inverted_index":{"We":[0],"obtain":[1],"a":[2],"complete":[3],"classification":[4],"of":[5,9],"all":[6],"self-adjoint":[7,37],"solution":[8],"the":[10,19,22,30],"control":[11],"algebraic":[12],"Riccati":[13,32],"equation":[14,33],"for":[15],"infinite-dimensional":[16],"systems":[17],"under":[18],"following":[20],"assumptions:":[21],"system":[23],"is":[24],"output":[25],"stabilizable,":[26],"strongly":[27],"detectable":[28],"and":[29],"filter":[31],"has":[34],"an":[35],"invertible":[36],"nonnegative":[38],"solution.":[39]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}