{"id":"https://openalex.org/W4294490333","doi":"https://doi.org/10.1080/00207179.2022.2120081","title":"Imaginary axis eigenvalues of Hamiltonian matrix: controllability, defectiveness and the \u03f5-characteristic","display_name":"Imaginary axis eigenvalues of Hamiltonian matrix: controllability, defectiveness and the \u03f5-characteristic","publication_year":2022,"publication_date":"2022-09-02","ids":{"openalex":"https://openalex.org/W4294490333","doi":"https://doi.org/10.1080/00207179.2022.2120081"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2022.2120081","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2022.2120081","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"article","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/A5030907068","display_name":"Ashish Kothyari","orcid":"https://orcid.org/0000-0002-4441-5844"},"institutions":[{"id":"https://openalex.org/I154851008","display_name":"Indian Institute of Technology Roorkee","ror":"https://ror.org/00582g326","country_code":"IN","type":"education","lineage":["https://openalex.org/I154851008"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ashish Kothyari","raw_affiliation_strings":["Electrical Engineering Department, Indian Institute of Technology Roorkee, Roorkee India"],"raw_orcid":"https://orcid.org/0000-0002-4441-5844","affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Indian Institute of Technology Roorkee, Roorkee India","institution_ids":["https://openalex.org/I154851008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042858792","display_name":"Chayan Bhawal","orcid":"https://orcid.org/0000-0003-3477-3725"},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Chayan Bhawal","raw_affiliation_strings":["Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, Guwahati India"],"raw_orcid":"https://orcid.org/0000-0003-3477-3725","affiliations":[{"raw_affiliation_string":"Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, Guwahati India","institution_ids":["https://openalex.org/I1317621060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004471796","display_name":"Madhu N. Belur","orcid":"https://orcid.org/0000-0002-1942-6293"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Madhu N. Belur","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0002-1942-6293","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022706065","display_name":"Debasattam Pal","orcid":"https://orcid.org/0000-0002-4886-3003"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debasattam Pal","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0002-4886-3003","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030907068"],"corresponding_institution_ids":["https://openalex.org/I154851008"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10730508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"96","issue":"12","first_page":"2958","last_page":"2975"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9990000128746033,"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/T13261","display_name":"Elasticity and Wave Propagation","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.7994582056999207},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7084393501281738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5550814867019653},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5229376554489136},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48518019914627075},{"id":"https://openalex.org/keywords/hamiltonian-matrix","display_name":"Hamiltonian matrix","score":0.4791761636734009},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42006540298461914},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.41657620668411255},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38425397872924805},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34694936871528625},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.34678518772125244},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.293168306350708},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18150022625923157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16439756751060486},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1521095633506775},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1122477650642395},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08199438452720642},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.0766112208366394}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7994582056999207},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7084393501281738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5550814867019653},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5229376554489136},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48518019914627075},{"id":"https://openalex.org/C135715101","wikidata":"https://www.wikidata.org/wiki/Q3299275","display_name":"Hamiltonian matrix","level":4,"score":0.4791761636734009},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42006540298461914},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.41657620668411255},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38425397872924805},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34694936871528625},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.34678518772125244},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.293168306350708},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18150022625923157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16439756751060486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1521095633506775},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1122477650642395},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08199438452720642},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0766112208366394},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2022.2120081","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2022.2120081","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G508971372","display_name":null,"funder_award_id":"15IRCCSG 012","funder_id":"https://openalex.org/F4320323448","funder_display_name":"Indian Institute of Technology Bombay"}],"funders":[{"id":"https://openalex.org/F4320323448","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W27481502","https://openalex.org/W1511275238","https://openalex.org/W1539689348","https://openalex.org/W1836001610","https://openalex.org/W1970391638","https://openalex.org/W1992243454","https://openalex.org/W2002357820","https://openalex.org/W2009602952","https://openalex.org/W2030854676","https://openalex.org/W2065313971","https://openalex.org/W2069863818","https://openalex.org/W2072305544","https://openalex.org/W2079179009","https://openalex.org/W2097327029","https://openalex.org/W2100548445","https://openalex.org/W2119218555","https://openalex.org/W2119886894","https://openalex.org/W2126479355","https://openalex.org/W2136596322","https://openalex.org/W2170336623","https://openalex.org/W2318665018","https://openalex.org/W2529488070","https://openalex.org/W2549690667","https://openalex.org/W2784878464","https://openalex.org/W2884915229","https://openalex.org/W2954565605","https://openalex.org/W2964030101","https://openalex.org/W3035578948","https://openalex.org/W4206092473","https://openalex.org/W4214672868","https://openalex.org/W4296477255","https://openalex.org/W4388319978","https://openalex.org/W6780383567"],"related_works":["https://openalex.org/W2091954099","https://openalex.org/W2049493903","https://openalex.org/W1976492425","https://openalex.org/W2110439450","https://openalex.org/W159432992","https://openalex.org/W1937292189","https://openalex.org/W2087544251","https://openalex.org/W2362292385","https://openalex.org/W2036459432","https://openalex.org/W1993093894"],"abstract_inverted_index":{"The":[0,47],"eigenstructure":[1],"of":[2,6,11,16,24,29,32,39,51,86,90,94,102,110,121,127,131,159,171,198,209,234,250,254,259,275,289,292],"imaginary":[3,91,137,168,184,201,251],"axis":[4,92,138,169,185,202,252],"eigenvalues":[5,93,139,170,186,253],"a":[7,40,77,95,218],"Hamiltonian":[8,26,64,78,96,117,133,173,220,236,255],"matrix":[9,79,97,134,174,221,256],"is":[10,67,178,222],"importance":[12],"in":[13,21,71,115,125,145,206,272],"many":[14],"fields":[15],"control":[17,58],"systems,":[18,27,45],"for":[19,43,55,80,148,180],"example,":[20,106],"stability":[22],"analysis":[23],"linear":[25],"computation":[28],"the":[30,63,81,111,116,122,132,136,146,149,156,167,172,195,199,207,273,290],"solutions":[31,124,181],"an":[33,56],"algebraic":[34],"Riccati":[35,263],"equation":[36],"(ARE),":[37],"existence":[38],"Lyapunov":[41,260],"function":[42],"LTI":[44],"etc.":[46],"dynamical":[48,75],"system":[49,65,82],"consisting":[50],"all":[52],"stationary":[53,113],"trajectories":[54,114],"optimal":[57],"problem":[59],"\u2013":[60,66],"often":[61],"called":[62],"known":[68],"to":[69,100,183,187,257,286],"admit,":[70],"its":[72,228],"state":[73],"space":[74],"equation,":[76],"matrix.":[83],"In":[84,241],"each":[85],"these":[87],"cases,":[88],"defectiveness":[89,107,249],"turns":[98],"out":[99],"be":[101],"crucial":[103],"importance.":[104],"For":[105],"causes":[108],"unboundedness":[109],"oscillatory":[112],"system.":[118],"A":[119],"characterisation":[120,208],"ARE":[123],"terms":[126],"Lagrangian":[128,210],"invariant":[129,211],"subspaces":[130],"when":[135],"are":[140,175],"defective":[141],"has":[142],"been":[143],"addressed":[144],"literature":[147],"controllable":[150,283],"case.":[151],"This":[152],"paper":[153,244],"focuses":[154],"on":[155,194],"general":[157],"case":[158],"uncontrollable":[160],"systems;":[161],"we":[162,231],"formulate":[163,214],"conditions":[164,193,215],"under":[165,216],"which":[166,217],"non-defective:":[176],"this":[177,204,243,293],"central":[179],"corresponding":[182],"not":[188],"become":[189],"unbounded.":[190],"We":[191,213,269],"provide":[192],"so-called":[196],"\u03f5-characteristic":[197,266],"non-defective":[200],"eigenvalue:":[203],"helps":[205],"subspaces.":[212],"passivity-based":[219],"normal":[223],"(i.e.":[224],"it":[225],"commutes":[226],"with":[227,238],"transpose),":[229],"and":[230,261,267,279,284],"link":[232,248],"normality":[233],"such":[235],"matrices":[237],"all-pass":[239],"behaviour.":[240],"summary,":[242],"formulates":[245],"results":[246,291],"that":[247],"solvabilities":[258],"Algebraic":[262],"equations,":[264],"controllability/observability,":[265],"sign-controllability.":[268],"consider":[270],"examples":[271],"area":[274],"bounded-real":[276],"transfer":[277],"functions":[278],"RLC":[280],"circuits,":[281],"both":[282],"uncontrollable,":[285],"study":[287],"applicability":[288],"paper.":[294]},"counts_by_year":[],"updated_date":"2026-06-18T08:10:14.011955","created_date":"2025-10-10T00:00:00"}