{"id":"https://openalex.org/W7104461103","doi":"https://doi.org/10.1155/jama/3745816","title":"A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory","display_name":"A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W7104461103","doi":"https://doi.org/10.1155/jama/3745816"},"language":"en","primary_location":{"id":"doi:10.1155/jama/3745816","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/3745816","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/3745816","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/3745816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Chacha Stephen Chacha","orcid":"https://orcid.org/0000-0001-8378-9219"},"institutions":[{"id":"https://openalex.org/I4210133744","display_name":"Iringa Mercy Organization","ror":"https://ror.org/041g4k048","country_code":"TZ","type":"nonprofit","lineage":["https://openalex.org/I4210133744"]}],"countries":["TZ"],"is_corresponding":true,"raw_author_name":"Chacha Stephen Chacha","raw_affiliation_strings":["Department of Mathematics ,  Physics and Informatics ,  Mkwawa University College of Education ,  Iringa ,  Tanzania , muce.ac.tz"],"raw_orcid":"https://orcid.org/0000-0001-8378-9219","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Physics and Informatics ,  Mkwawa University College of Education ,  Iringa ,  Tanzania , muce.ac.tz","institution_ids":["https://openalex.org/I4210133744"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210133744"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.9555,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.82309215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9902999997138977,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9902999997138977,"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 methods for differential equations","score":0.0017000000225380063,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.00139999995008111,"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7050999999046326},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6482999920845032},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4562999904155731},{"id":"https://openalex.org/keywords/relevance","display_name":"Relevance (law)","score":0.4505999982357025},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4458000063896179},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4156999886035919},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.38830000162124634},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.38600000739097595},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.38089999556541443}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7050999999046326},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6482999920845032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5422000288963318},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5360999703407288},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4562999904155731},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.4505999982357025},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4156999886035919},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.38830000162124634},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.38089999556541443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37880000472068787},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.3776000142097473},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C175197506","wikidata":"https://www.wikidata.org/wiki/Q1003225","display_name":"Measure-preserving dynamical system","level":5,"score":0.352400004863739},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.34950000047683716},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.34299999475479126},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.3231000006198883},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.31439998745918274},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27129998803138733},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/jama/3745816","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/3745816","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/3745816","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5c669fa819fa40889ccda6a79a0ea80f","is_oa":true,"landing_page_url":"https://doaj.org/article/5c669fa819fa40889ccda6a79a0ea80f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/jama/3745816","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/3745816","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/3745816","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7104461103.pdf","grobid_xml":"https://content.openalex.org/works/W7104461103.grobid-xml"},"referenced_works_count":79,"referenced_works":["https://openalex.org/W92560179","https://openalex.org/W847047041","https://openalex.org/W1548589512","https://openalex.org/W1564791200","https://openalex.org/W1963671427","https://openalex.org/W1969644204","https://openalex.org/W1975443030","https://openalex.org/W1997054581","https://openalex.org/W2008430533","https://openalex.org/W2020804487","https://openalex.org/W2026745826","https://openalex.org/W2037253724","https://openalex.org/W2047277813","https://openalex.org/W2054390548","https://openalex.org/W2058812457","https://openalex.org/W2061564552","https://openalex.org/W2097634708","https://openalex.org/W2099629311","https://openalex.org/W2120627211","https://openalex.org/W2126999002","https://openalex.org/W2136556155","https://openalex.org/W2142926274","https://openalex.org/W2724330217","https://openalex.org/W2799960778","https://openalex.org/W2886530724","https://openalex.org/W2899121548","https://openalex.org/W2906827207","https://openalex.org/W2907708421","https://openalex.org/W2913524003","https://openalex.org/W2972401824","https://openalex.org/W2994446770","https://openalex.org/W3015067004","https://openalex.org/W3023586494","https://openalex.org/W3024960524","https://openalex.org/W3025721496","https://openalex.org/W3026168046","https://openalex.org/W3038118776","https://openalex.org/W3094908693","https://openalex.org/W3095073546","https://openalex.org/W3110833271","https://openalex.org/W3114992681","https://openalex.org/W3163693668","https://openalex.org/W3163993681","https://openalex.org/W3164857342","https://openalex.org/W3194003300","https://openalex.org/W3200756715","https://openalex.org/W3211552519","https://openalex.org/W3216703346","https://openalex.org/W4205749448","https://openalex.org/W4206504834","https://openalex.org/W4212764296","https://openalex.org/W4213414248","https://openalex.org/W4214583387","https://openalex.org/W4235019172","https://openalex.org/W4242769917","https://openalex.org/W4248463091","https://openalex.org/W4281253162","https://openalex.org/W4285030028","https://openalex.org/W4285061417","https://openalex.org/W4285739801","https://openalex.org/W4286781802","https://openalex.org/W4294690151","https://openalex.org/W4319072945","https://openalex.org/W4323825473","https://openalex.org/W4381468923","https://openalex.org/W4387827545","https://openalex.org/W4388549473","https://openalex.org/W4390412507","https://openalex.org/W4390871384","https://openalex.org/W4392298624","https://openalex.org/W4396848921","https://openalex.org/W4401539085","https://openalex.org/W4401632506","https://openalex.org/W4402585092","https://openalex.org/W4402644538","https://openalex.org/W4403277463","https://openalex.org/W4403768163","https://openalex.org/W4407087725","https://openalex.org/W4415978566"],"related_works":[],"abstract_inverted_index":{"Matrix":[0],"equations":[1],"are":[2,71,96],"of":[3,12,20,57],"foundational":[4],"importance":[5],"in":[6,28],"the":[7,49,55,89],"modeling,":[8],"investigation,":[9],"and":[10,25,31,38,48,54,68,79,93,101],"control":[11,29],"dynamical":[13,32],"systems.":[14,33],"This":[15],"review":[16],"discusses":[17],"various":[18],"classes":[19],"matrix":[21],"equations,":[22,40],"their":[23,26,74],"solutions,":[24],"relevance":[27],"theory":[30],"Key":[34],"topics":[35],"include":[36],"Lyapunov":[37],"Riccati":[39],"iterative":[41],"techniques":[42],"such":[43,85],"as":[44,86],"Krylov":[45],"subspace":[46],"approaches":[47],"alternating":[50],"direction":[51],"implicit":[52],"technique,":[53],"influence":[56],"condition":[58],"numbers":[59],"on":[60,76],"numerical":[61],"robustness.":[62],"In":[63],"addition,":[64],"model\u2010order":[65],"reduction":[66],"methods":[67],"reduced\u2010order":[69],"models":[70],"examined":[72],"for":[73,103],"impact":[75],"transient":[77],"behavior":[78],"computational":[80],"efficiency.":[81],"Finally,":[82],"emerging":[83],"directions":[84],"data\u2010driven":[87],"methodologies,":[88],"Koopman":[90],"operator":[91],"perspective,":[92],"quantum":[94],"computing":[95],"explored,":[97],"alongside":[98],"outstanding":[99],"challenges":[100],"prospects":[102],"future":[104],"research.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-11-09T00:00:00"}