{"id":"https://openalex.org/W2521529097","doi":"https://doi.org/10.1007/s11045-016-0454-8","title":"On the connection between discrete linear repetitive processes and 2-D discrete linear systems","display_name":"On the connection between discrete linear repetitive processes and 2-D discrete linear systems","publication_year":2016,"publication_date":"2016-09-19","ids":{"openalex":"https://openalex.org/W2521529097","doi":"https://doi.org/10.1007/s11045-016-0454-8","mag":"2521529097"},"language":"en","primary_location":{"id":"doi:10.1007/s11045-016-0454-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11045-016-0454-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11045-016-0454-8.pdf","source":{"id":"https://openalex.org/S198285748","display_name":"Multidimensional Systems and Signal Processing","issn_l":"0923-6082","issn":["0923-6082","1573-0824"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multidimensional Systems and Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs11045-016-0454-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088968414","display_name":"Mohamed S. Boudellioua","orcid":"https://orcid.org/0000-0001-8805-1416"},"institutions":[{"id":"https://openalex.org/I47818738","display_name":"Sultan Qaboos University","ror":"https://ror.org/04wq8zb47","country_code":"OM","type":"education","lineage":["https://openalex.org/I47818738"]}],"countries":["OM"],"is_corresponding":false,"raw_author_name":"M. S. Boudellioua","raw_affiliation_strings":["Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman","institution_ids":["https://openalex.org/I47818738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066492464","display_name":"Krzysztof Ga\u0142kowski","orcid":"https://orcid.org/0000-0003-4470-2162"},"institutions":[{"id":"https://openalex.org/I46305939","display_name":"University of Zielona G\u00f3ra","ror":"https://ror.org/04fzm7v55","country_code":"PL","type":"education","lineage":["https://openalex.org/I46305939"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"K. Galkowski","raw_affiliation_strings":["Institute of Control and Computation Engineering, University of Zielona Gora, Zielona Gora, Poland"],"raw_orcid":"https://orcid.org/0000-0003-4470-2162","affiliations":[{"raw_affiliation_string":"Institute of Control and Computation Engineering, University of Zielona Gora, Zielona Gora, Poland","institution_ids":["https://openalex.org/I46305939"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081788754","display_name":"Eric Rogers","orcid":"https://orcid.org/0000-0003-0179-9398"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"E. Rogers","raw_affiliation_strings":["Department of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066492464"],"corresponding_institution_ids":["https://openalex.org/I46305939"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":2.902,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.90628542,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"28","issue":"1","first_page":"341","last_page":"351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11749","display_name":"Iterative Learning Control Systems","score":0.9968000054359436,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9968000054359436,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9933000206947327,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.712833046913147},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.7085232734680176},{"id":"https://openalex.org/keywords/transformation-matrix","display_name":"Transformation matrix","score":0.5506293177604675},{"id":"https://openalex.org/keywords/companion-matrix","display_name":"Companion matrix","score":0.5415605902671814},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.5313190817832947},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.514470100402832},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5077841877937317},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5045732259750366},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"Characteristic polynomial","score":0.49758651852607727},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.4958063066005707},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4914144277572632},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4425412118434906},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4348664879798889},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.43061894178390503},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4198307693004608},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3934205174446106},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3811383843421936},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3109060525894165},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.25030869245529175},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09204277396202087},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08238339424133301},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08224302530288696}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.712833046913147},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.7085232734680176},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.5506293177604675},{"id":"https://openalex.org/C141495983","wikidata":"https://www.wikidata.org/wiki/Q814361","display_name":"Companion matrix","level":5,"score":0.5415605902671814},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.5313190817832947},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.514470100402832},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5077841877937317},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5045732259750366},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.49758651852607727},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.4958063066005707},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4914144277572632},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4425412118434906},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4348664879798889},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.43061894178390503},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4198307693004608},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3934205174446106},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3811383843421936},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3109060525894165},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.25030869245529175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09204277396202087},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08238339424133301},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08224302530288696},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"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/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11045-016-0454-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11045-016-0454-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11045-016-0454-8.pdf","source":{"id":"https://openalex.org/S198285748","display_name":"Multidimensional Systems and Signal Processing","issn_l":"0923-6082","issn":["0923-6082","1573-0824"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multidimensional Systems and Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:403773","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s11045-016-0454-8>).","pdf_url":"https://eprints.soton.ac.uk/403773/1/publishedver.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s11045-016-0454-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11045-016-0454-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11045-016-0454-8.pdf","source":{"id":"https://openalex.org/S198285748","display_name":"Multidimensional Systems and Signal Processing","issn_l":"0923-6082","issn":["0923-6082","1573-0824"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multidimensional Systems and Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322573","display_name":"Sultan Qaboos University","ror":"https://ror.org/04wq8zb47"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2521529097.pdf","grobid_xml":"https://content.openalex.org/works/W2521529097.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W130632564","https://openalex.org/W433972222","https://openalex.org/W1989867972","https://openalex.org/W2000301461","https://openalex.org/W2042710540","https://openalex.org/W2044087234","https://openalex.org/W2047216730","https://openalex.org/W2061284051","https://openalex.org/W2080920148","https://openalex.org/W2085849252","https://openalex.org/W2100038940","https://openalex.org/W2103759780","https://openalex.org/W2104247012","https://openalex.org/W2121759998","https://openalex.org/W2157192413","https://openalex.org/W2802087291","https://openalex.org/W6672251385"],"related_works":["https://openalex.org/W2905919007","https://openalex.org/W2575230999","https://openalex.org/W2335071938","https://openalex.org/W1985103827","https://openalex.org/W2078782009","https://openalex.org/W1999630301","https://openalex.org/W2040308058","https://openalex.org/W2062371205","https://openalex.org/W2017904880","https://openalex.org/W2521529097"],"abstract_inverted_index":{"A":[0],"direct":[1],"method":[2],"is":[3,40,57],"developed":[4],"that":[5,24,42],"reduces":[6],"a":[7,12,18],"polynomial":[8,48],"system":[9,35,49,60,68],"matrix":[10,50,69],"describing":[11],"discrete":[13],"linear":[14],"repetitive":[15],"process":[16],"to":[17],"2-D":[19,54],"singular":[20,55,71],"state-space":[21],"form":[22,56,72],"such":[23],"all":[25],"the":[26,30,34,43,46,66,74],"relevant":[27],"properties,":[28],"including":[29],"zero":[31,58],"structure":[32],"of":[33,65],"matrix,":[36],"are":[37,77],"retained.":[38],"It":[39],"shown":[41],"transformation":[44,75],"linking":[45],"original":[47],"with":[51],"its":[52],"associated":[53],"coprime":[59],"equivalence.":[61],"The":[62],"exact":[63],"nature":[64],"resulting":[67],"in":[70],"and":[73],"involved":[76],"established.":[78]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}