{"id":"https://openalex.org/W2727988678","doi":"https://doi.org/10.1137/16m1057516","title":"On the Kronecker Canonical Form of Singular Mixed Matrix Pencils","display_name":"On the Kronecker Canonical Form of Singular Mixed Matrix Pencils","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2727988678","doi":"https://doi.org/10.1137/16m1057516","mag":"2727988678"},"language":"en","primary_location":{"id":"doi:10.1137/16m1057516","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1057516","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5040460257","display_name":"Satoru Iwata","orcid":"https://orcid.org/0000-0002-6467-1335"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Satoru Iwata","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075575637","display_name":"Mizuyo Takamatsu","orcid":"https://orcid.org/0000-0002-8048-6439"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mizuyo Takamatsu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2245,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8038545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"55","issue":"3","first_page":"2134","last_page":"2150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9962000250816345,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9962000250816345,"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/T13286","display_name":"Modeling and Simulation Systems","score":0.9927999973297119,"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":0.9861999750137329,"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/mathematics","display_name":"Mathematics","score":0.8533947467803955},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.7686166763305664},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.7290714979171753},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.6795765161514282},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.5923329591751099},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.55039381980896},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5138850212097168},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.45261579751968384},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.43523120880126953},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.42494675517082214},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4189510941505432},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4161326289176941},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.41094809770584106},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4094852805137634},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3890284597873688}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8533947467803955},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7686166763305664},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.7290714979171753},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.6795765161514282},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.5923329591751099},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.55039381980896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5138850212097168},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.45261579751968384},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.43523120880126953},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42494675517082214},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4189510941505432},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4161326289176941},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.41094809770584106},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4094852805137634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3890284597873688},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1057516","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1057516","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G6978880808","display_name":null,"funder_award_id":"25730009","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320334789","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W192807697","https://openalex.org/W430666788","https://openalex.org/W637320825","https://openalex.org/W849556615","https://openalex.org/W1509586029","https://openalex.org/W1533712308","https://openalex.org/W1555104280","https://openalex.org/W1556970733","https://openalex.org/W1964957373","https://openalex.org/W1983438352","https://openalex.org/W1984452258","https://openalex.org/W1985910458","https://openalex.org/W1989266286","https://openalex.org/W1995504856","https://openalex.org/W1996965151","https://openalex.org/W2008256634","https://openalex.org/W2009983789","https://openalex.org/W2013474260","https://openalex.org/W2017073440","https://openalex.org/W2018158936","https://openalex.org/W2019609727","https://openalex.org/W2020927880","https://openalex.org/W2022412951","https://openalex.org/W2025362408","https://openalex.org/W2034698420","https://openalex.org/W2035684525","https://openalex.org/W2036705738","https://openalex.org/W2066944191","https://openalex.org/W2067824344","https://openalex.org/W2068844468","https://openalex.org/W2085849252","https://openalex.org/W2090223047","https://openalex.org/W2094372481","https://openalex.org/W2095848239","https://openalex.org/W2097178696","https://openalex.org/W2128978199","https://openalex.org/W2142433871","https://openalex.org/W2153132823","https://openalex.org/W2157184494","https://openalex.org/W2296217093","https://openalex.org/W2785187072","https://openalex.org/W2971043731"],"related_works":["https://openalex.org/W1995821805","https://openalex.org/W2142043165","https://openalex.org/W2120296059","https://openalex.org/W1973845752","https://openalex.org/W2989988396","https://openalex.org/W3103732277","https://openalex.org/W2770308590","https://openalex.org/W2091170701","https://openalex.org/W1996965151","https://openalex.org/W2119459069"],"abstract_inverted_index":{"Consider":[0],"a":[1,65,76,100],"linear":[2],"time-invariant":[3],"dynamical":[4],"system":[5,48,114],"that":[6,31,39],"can":[7],"be":[8],"described":[9],"as":[10],"$F\\dot{x}(t)":[11],"=A{x}(t)+B{u}(t)$,":[12],"where":[13],"$A$,":[14],"$B$,":[15],"and":[16,36],"$F$":[17],"are":[18],"mixed":[19,59,93],"matrices,":[20],"i.e.,":[21],"matrices":[22],"having":[23],"two":[24],"kinds":[25],"of":[26,46,57,79,82,87,92,108],"nonzero":[27],"coefficients:":[28],"fixed":[29],"constants":[30],"account":[32],"for":[33,103,112],"conservation":[34],"laws":[35],"independent":[37],"parameters":[38],"represent":[40],"physical":[41],"characteristics.":[42],"The":[43,96],"controllable":[44,110],"subspace":[45,111],"the":[47,53,58,71,80,83,88,106,109,113],"is":[49],"closely":[50],"related":[51],"to":[52,99],"Kronecker":[54,89],"canonical":[55,90],"form":[56,91],"matrix":[60,94],"pencil":[61],"$\\begin{pmatrix}A-sF\\mid":[62],"B\\end{pmatrix}$.":[63],"Under":[64],"physically":[66],"meaningful":[67],"assumption":[68],"justified":[69],"by":[70],"dimensional":[72],"analysis,":[73],"we":[74],"provide":[75],"combinatorial":[77],"characterization":[78,97],"sums":[81],"minimal":[84],"row/column":[85],"indices":[86],"pencils.":[95],"leads":[98],"matroid-theoretic":[101],"algorithm":[102],"efficiently":[104],"computing":[105],"dimension":[107],"with":[115],"nonsingular":[116],"$F$.":[117]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
