{"id":"https://openalex.org/W7156834848","doi":"https://doi.org/10.48550/arxiv.2604.23895","title":"Isospectral Steering","display_name":"Isospectral Steering","publication_year":2026,"publication_date":"2026-04-26","ids":{"openalex":"https://openalex.org/W7156834848","doi":"https://doi.org/10.48550/arxiv.2604.23895"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.23895","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23895","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.23895","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093497269","display_name":"Ralph Sabbagh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sabbagh, Ralph","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035194316","display_name":"Tryphon T. Georgiou","orcid":"https://orcid.org/0000-0003-0012-5447"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georgiou, Tryphon T.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.42750000953674316,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.42750000953674316,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.06870000064373016,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.03460000082850456,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/isospectral","display_name":"Isospectral","score":0.8884000182151794},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.6205000281333923},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6065999865531921},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.44519999623298645},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4417000114917755},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4133000075817108},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.40860000252723694},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3937000036239624},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.38199999928474426},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3806999921798706}],"concepts":[{"id":"https://openalex.org/C2779710842","wikidata":"https://www.wikidata.org/wiki/Q6086323","display_name":"Isospectral","level":2,"score":0.8884000182151794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7429999709129333},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.6205000281333923},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6065999865531921},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.44519999623298645},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4417000114917755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4212999939918518},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4133000075817108},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.38199999928474426},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.36039999127388},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3140000104904175},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3098999857902527},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.26159998774528503},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.23895","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23895","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.23895","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23895","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7962636947631836,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,5,36,39,78,91,104,125],"controllability":[3],"of":[4,12,38,55,75,86,94,103],"differential":[6],"Lyapunov":[7],"equation":[8],"under":[9],"isospectral":[10,87],"rotation":[11],"a":[13,22,52,70],"linear":[14,122],"gradient":[15],"field.":[16],"Specifically,":[17],"control":[18,56],"is":[19,111],"effected":[20],"by":[21,33,69],"symmetric":[23],"time-varying":[24],"gain-matrix":[25],"constrained":[26],"to":[27,61,114,120],"have":[28],"fixed":[29],"eigenvalues;":[30],"that":[31],"is,":[32],"exclusively":[34],"modulating":[35],"eigen-vectors":[37],"state":[40],"matrix":[41],"and":[42,82,89,101,124],"not":[43],"its":[44],"eigenvalues.":[45,76],"Motivation":[46],"for":[47,96,129],"this":[48,84],"problem":[49],"stems":[50],"from":[51],"certain":[53],"type":[54,85],"objectives":[57],"(minimum":[58],"shear/attention)":[59],"aimed":[60],"reduce":[62],"anisotropic":[63],"deformation":[64],"when":[65],"ensembles":[66],"are":[67],"steered":[68],"common":[71],"law--optimality":[72],"necessitates":[73],"constancy":[74],"In":[77],"paper":[79],"we":[80,109],"introduce":[81],"motivate":[83],"steering,":[88],"describe":[90],"reachable":[92],"set":[93],"covariances":[95],"any":[97],"specified":[98],"terminal":[99],"time":[100],"eigenvalues":[102],"gain":[105],"matrix.":[106],"The":[107],"theory":[108],"develop":[110],"intimately":[112],"linked":[113],"multilinear":[115],"algebra":[116,123],"as":[117,119],"well":[118],"positive":[121],"Birkoff-von":[126],"Neumann":[127],"theorem":[128],"doubly":[130],"stochastic":[131],"matrices.":[132]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-29T00:00:00"}
