{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T01:05:12Z","timestamp":1787360712012,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>In this paper we solve the problem of the existence of rational realizations of response maps. Sufficient and necessary conditions for a response map to be realizable by a rational system are presented. We provide also the characterization of the existence of rationally observable and canonical rational realizations for a given response map.<\/jats:p>","DOI":"10.1137\/080714506","type":"journal-article","created":{"date-parts":[[2009,10,14]],"date-time":"2009-10-14T18:08:52Z","timestamp":1255543732000},"page":"2840-2856","source":"Crossref","is-referenced-by-count":22,"title":["Realization Theory for Rational Systems: The Existence of Rational Realizations"],"prefix":"10.1137","volume":"48","author":[{"given":"Jana","family":"N\u011bmcov\u00e1","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan H.","family":"van Schuppen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,10,14]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Z. Bartosiewicz,\n                      Realizations of polynomial systems\n                      , in Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazenwinkel, eds., D. Reidel, Dordrecht, 1986, pp. 45\u201354.","DOI":"10.1007\/978-94-009-4706-1_3"},{"key":"R2","first-page":"13","volume":"35","author":"Bartosiewicz Z.","year":"1987","journal-title":"Bull. Pol. Acad. Sci. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0239-7269","issn-type":"print"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(87)90066-1"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551285"},{"key":"R5","unstructured":"N. Bourbaki,\n                      Algebra\n                      II:\n                      Chapters\n                      4\u20137, Elem. Math. (Berlin), Springer-Verlag, Berlin, 1990."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.2307\/2373982"},{"key":"R7","unstructured":"D. Cox, J. Little, and D. O'Shea,\n                      Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra\n                      , 3rd ed., Springer-Verlag, Berlin, 2007."},{"key":"R8","unstructured":"P. Falb,\n                      Methods of Algebraic Geometry in Control Theory: Part 1, Scalar Linear Systems and Affine Algebraic Geometry\n                      , Birkh\u00e4user, Boston, 1990."},{"key":"R9","unstructured":"P. Falb,\n                      Methods of Algebraic Geometry in Control Theory: Part 2, Multivariable Linear Systems and Projective Algebraic Geometry\n                      , Birkh\u00e4user, Boston, 1999."},{"key":"R10","unstructured":"N. Jacobson,\n                      Basic Algebra\n                      II, W. H. Freeman, San Francisco, 1980."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0318034"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"E. Kunz,\n                      Introduction to Commutative Algebra and Algebraic Geometry\n                      , Birkh\u00e4user, Boston, 1985.","DOI":"10.1007\/978-1-4612-5290-0"},{"key":"R13","unstructured":"S. Lang,\n                      Algebra\n                      , Addison-Wesley, Reading, MA, 1965."},{"key":"R14","doi-asserted-by":"crossref","unstructured":"J. N\u011bmcov\u00e1,\n                      Algebraic reachability of rational systems\n                      , in Proceedings of European Control Conference, Budapest, Hungary, 2009.","DOI":"10.23919\/ECC.2009.7074414"},{"key":"R15","unstructured":"J. N\u011bmcov\u00e1 and J.H. van Schuppen,\n                      Realization theory for rational systems: Minimal rational realizations\n                      , Acta Appl. Math., to appear."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"E.D. Sontag,\n                      Polynomial Response Maps\n                      , Lecture Notes in Control and Inform. 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Samuel,\n                      Commutative Algebra\n                      I, II, Springer-Verlag, Berlin, 1958."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080714506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:52:35Z","timestamp":1787316755000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080714506"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/080714506"],"URL":"https:\/\/doi.org\/10.1137\/080714506","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}