{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T08:57:13Z","timestamp":1653987433433},"reference-count":15,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T00:00:00Z","timestamp":1567036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>It is well known that given the continuous-time AutoRegressive representation $A\\left ( \\rho \\right ) \\beta \\left ( t\\right ) =0,$ where $\\rho $ denotes the differential operator and $A\\left ( \\rho \\right ) $ a regular polynomial matrix, we can always construct the smooth behaviour of this system, by using the finite zero structure of $A\\left ( \\rho \\right ) $. The main theme of this work is to study the following inverse problem: given a specific smooth behaviour, find a family of regular polynomial matrices $A\\left ( \\rho \\right ) $, such that the system $A\\left ( \\rho \\right ) \\beta \\left ( t\\right ) =0$ has exactly the prescribed behaviour. Following an idea coming from Antoulas &amp; Willems (1993) and Willems (1986, 1991) we present an algorithm which solve this problem and can be easily implemented either in a computer programming language like C++ or in a computer algebra system like Mathematica.<\/jats:p>","DOI":"10.1093\/imamci\/dnz021","type":"journal-article","created":{"date-parts":[[2019,6,17]],"date-time":"2019-06-17T11:09:51Z","timestamp":1560769791000},"page":"730-751","source":"Crossref","is-referenced-by-count":1,"title":["On the exact modelling of linear systems"],"prefix":"10.1093","volume":"37","author":[{"given":"Georgia G","family":"Pechlivanidou","sequence":"first","affiliation":[]},{"given":"Nicholas P","family":"Karampetakis","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}]}],"member":"286","published-online":{"date-parts":[[2019,8,29]]},"reference":[{"key":"2021060109591923800_ref2","doi-asserted-by":"crossref","first-page":"1776","DOI":"10.1109\/9.250557","article-title":"A behavioral approach to linear exact modeling","volume":"38","author":"Antoulas","year":"1993","journal-title":"IEEE Trans. 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Theory"},{"key":"2021060109591923800_ref14","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1515\/amcs-2017-0002","article-title":"Construction of algebraic and difference equations with prescribed solution space","volume":"27","author":"Moysis","year":"2017","journal-title":"Int. J. Appl. Math. Comp. Sci."},{"key":"2021060109591923800_ref15","first-page":"2096","article-title":"A duality perspective on Loewner interpolation","volume-title":"Proc. 56th IEEE Conference on Decision and Control (CDC)","author":"Rapisarda","year":"2015"},{"key":"2021060109591923800_ref16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-21003-2_2","article-title":"Bilinear differential forms and the Loewner framework for rational interpolation","volume-title":"Mathematical Control Theory II","author":"Rapisarda","year":"2015"},{"key":"2021060109591923800_ref18","volume-title":"Linear Multivariable Control Algebraic Analysis And Synthesis Methods","author":"Vardulakis","year":"1991"},{"key":"2021060109591923800_ref19","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1016\/0005-1098(86)90005-1","article-title":"From time series to linear system\u2014part II. 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Control Optim."},{"key":"2021060109591923800_ref22","article-title":"Recursive computation of the multidimensional MPUM","volume-title":"Proceedings of the 17th International Symposium on Mathematical Theory Networks Systems (MTNS)","author":"Zerz","year":"2006"},{"key":"2021060109591923800_ref23","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s11045-007-0043-y","article-title":"The discrete multidimensional MPUM","volume":"19","author":"Zerz","year":"2008","journal-title":"Multidimens. Syst. Signal Process."},{"key":"2021060109591923800_ref24","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s11045-010-0125-0","article-title":"Exact linear modeling with polynomial coefficients","volume":"22","author":"Zerz","year":"2011","journal-title":"Multidimens. Syst. Signal Process."}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/3\/730\/38390469\/imamci_37_3_730.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/3\/730\/38390469\/imamci_37_3_730.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T10:19:34Z","timestamp":1622542774000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/37\/3\/730\/5553670"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,29]]},"references-count":15,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,8,29]]},"published-print":{"date-parts":[[2020,9,16]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnz021","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"value":"0265-0754","type":"print"},{"value":"1471-6887","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,9]]},"published":{"date-parts":[[2019,8,29]]}}}