{"id":"https://openalex.org/W7214577704","doi":"https://doi.org/10.48550/arxiv.2609.31044","title":"Operator-ADI balanced truncation of delay differential systems","display_name":"Operator-ADI balanced truncation of delay differential systems","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214577704","doi":"https://doi.org/10.48550/arxiv.2609.31044"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31044","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31044","pdf_url":"https://arxiv.org/pdf/2609.31044","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.31044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027602749","display_name":"Timo Reis","orcid":"https://orcid.org/0000-0003-0721-8494","observed_orcids":["https://orcid.org/0000-0003-0721-8494"]},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Reis, Timo","raw_affiliation_strings":["Technische Universit\u00e4t Ilmenau , Ilmenau , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Ilmenau , Ilmenau , Germany","institution_ids":["https://openalex.org/I119449181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027602749"],"corresponding_institution_ids":["https://openalex.org/I119449181"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.8080999851226807,"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/T11081","display_name":"Advanced Control Systems Design","score":0.8080999851226807,"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":0.06809999793767929,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.05959999933838844,"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/balanced-truncation","display_name":"balanced truncation","score":0.9390000104904175},{"id":"https://openalex.org/keywords/delay-differential-equations","display_name":"delay differential equations","score":0.9419999718666077},{"id":"https://openalex.org/keywords/hankel-singular-values","display_name":"Hankel singular values","score":0.8980000019073486},{"id":"https://openalex.org/keywords/model-reduction","display_name":"model reduction","score":0.621999979019165},{"id":"https://openalex.org/keywords/discrete-delay","display_name":"discrete delay","score":0.5809999704360962}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7631999850273132},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.5705999732017517},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5504999756813049},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5239999890327454},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5077999830245972},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.503600001335144},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4731999933719635},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.46959999203681946},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.45890000462532043},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4375999867916107},{"id":"https://openalex.org/C205609532","wikidata":"https://www.wikidata.org/wiki/Q770324","display_name":"Minimal realization","level":3,"score":0.41290000081062317},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.34130001068115234},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.30090001225471497},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.29750001430511475},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.2572999894618988}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31044","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31044","pdf_url":"https://arxiv.org/pdf/2609.31044","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2609.31044","doi":"https://doi.org/10.48550/arxiv.2609.31044","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31044","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.31044","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31044","pdf_url":"https://arxiv.org/pdf/2609.31044","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214577704.pdf","grobid_xml":"https://content.openalex.org/works/W7214577704.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W142952862","https://openalex.org/W203646022","https://openalex.org/W590413840","https://openalex.org/W1494118823","https://openalex.org/W1538686203","https://openalex.org/W1607633954","https://openalex.org/W1973337814","https://openalex.org/W1978943241","https://openalex.org/W1984813610","https://openalex.org/W2018057661","https://openalex.org/W2021881468","https://openalex.org/W2023322178","https://openalex.org/W2034380464","https://openalex.org/W2063515500","https://openalex.org/W2066059560","https://openalex.org/W2067885292","https://openalex.org/W2067958186","https://openalex.org/W2071861954","https://openalex.org/W2076656421","https://openalex.org/W2092560650","https://openalex.org/W2104744926","https://openalex.org/W2116187428","https://openalex.org/W2122967867","https://openalex.org/W2149971042","https://openalex.org/W2156464932","https://openalex.org/W2323341019","https://openalex.org/W2506632866","https://openalex.org/W2991009190","https://openalex.org/W4236550665","https://openalex.org/W4399555005"],"related_works":["https://openalex.org/W4293652230","https://openalex.org/W1964328379","https://openalex.org/W7118159821","https://openalex.org/W1991518260","https://openalex.org/W2783292330","https://openalex.org/W2116187428","https://openalex.org/W4406317141","https://openalex.org/W2155068038","https://openalex.org/W2219148655","https://openalex.org/W4416526651"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,13,69,92],"balanced":[3,113],"truncation":[4,114],"method":[5,26,131],"for":[6,19],"linear":[7,64],"delay":[8,39],"differential":[9],"systems":[10],"based":[11],"on":[12,29,87],"finite-rank":[14,47],"alternating-direction":[15],"implicit":[16],"(ADI)":[17],"iteration":[18],"the":[20,30,38,59,78,88,95,106,116,130,142],"associated":[21],"operator":[22],"Lyapunov":[23],"equations.":[24],"The":[25,46,119,136],"acts":[27],"directly":[28],"infinite-dimensional":[31,117],"history-state":[32],"realization":[33],"and":[34,49,91],"does":[35],"not":[36],"discretize":[37],"interval":[40],"during":[41],"Gramian":[42],"approximation":[43],"or":[44],"balancing.":[45],"reachability":[48],"observability":[50],"factors":[51,67],"are":[52],"represented":[53],"exactly":[54],"in":[55,81,94,102,141],"Takenaka--Malmquist":[56],"coordinates,":[57],"reducing":[58],"required":[60],"computations":[61],"to":[62,105,122],"finite-dimensional":[63],"algebra.":[65],"These":[66],"yield":[68],"finite-dimensional,":[70],"delay-free":[71],"reduced":[72,107],"model.":[73],"For":[74],"real":[75,82],"system":[76],"data,":[77],"implementation":[79,139],"remains":[80],"arithmetic.":[83],"Under":[84],"suitable":[85],"conditions":[86],"ADI":[89],"shifts":[90],"gap":[93],"Hankel":[96],"singular":[97],"values,":[98],"we":[99],"prove":[100],"convergence":[101],"$\\mathcal":[103],"H_\\infty$":[104],"transfer":[108],"function":[109],"obtained":[110],"by":[111],"exact":[112],"of":[115],"system.":[118],"construction":[120],"extends":[121],"finitely":[123],"many":[124],"discrete":[125],"delays.":[126],"Numerical":[127],"experiments":[128,143],"validate":[129],"against":[132],"independent":[133],"reference":[134],"computations.":[135],"complete":[137],"MATLAB":[138],"used":[140],"is":[144],"provided":[145],"as":[146],"supplementary":[147],"material.":[148]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-29T00:00:00"}