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In this paper, the equivalence problems on several classes of bivariate polynomial matrices are investigated. Some new results on the equivalence of these matrices are obtained. These results are useful for reducing two\u2010dimensional systems.<\/jats:p>","DOI":"10.1155\/2021\/6911443","type":"journal-article","created":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T00:50:06Z","timestamp":1637196606000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Further Results on the Reduction of Two\u2010Dimensional Systems"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3444-8861","authenticated-orcid":false,"given":"Dongmei","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1235-0617","authenticated-orcid":false,"given":"Yingying","family":"Gui","sequence":"additional","affiliation":[]},{"given":"Jinwang","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Man","family":"Wu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,11,17]]},"reference":[{"volume-title":"Applied Multidimensional Systems Theory","year":"1982","author":"Bose N.","key":"e_1_2_9_1_2"},{"volume-title":"Multidimensional Systems Theory and Applications","year":"2003","author":"Bose N.","key":"e_1_2_9_2_2"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2019.10.031"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.06.036"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2020.04.051"},{"volume-title":"State Space and Multivariate Theory","year":"1970","author":"Rosenbrock H.","key":"e_1_2_9_6_2"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207177808922487"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.1983.1103118"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207178608933558"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.4236\/ajcm.2012.21003"},{"key":"e_1_2_9_11_2","first-page":"1983","article-title":"Some further results on the Smith form of bivariate polynomial matrices","volume":"39","author":"Li D.","year":"2019","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2017.04.015"},{"key":"e_1_2_9_13_2","unstructured":"LinZ. 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On the equivalence and factorization of multivariate polynomial matrices Proceedings of the IEEE November 2006 Tampa FL USA 4911\u20134914."},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11045-015-0329-4"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf01390008"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/7435237"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.04.020"},{"key":"e_1_2_9_18_2","first-page":"543","article-title":"Further results on the equivalence to Smith form of multivariate polynomial matrices","volume":"42","author":"Boudellioua M.","year":"2013","journal-title":"Control and Cybernetics"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/5430842"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6911443.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6911443.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/6911443","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:30:57Z","timestamp":1723242657000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/6911443"}},"subtitle":[],"editor":[{"given":"Xiao Ling","family":"Wang","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/6911443"],"URL":"https:\/\/doi.org\/10.1155\/2021\/6911443","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-08-05","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-10-29","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-11-17","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6911443"}}