{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:43:47Z","timestamp":1709203427030},"reference-count":18,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,3,1]]},"abstract":"<jats:title>On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems<\/jats:title><jats:p>We review the realization theory of polynomial (transfer function) matrices via \"pure\" generalized state space system models. The concept of an<jats:italic>irreducible-at-infinity<\/jats:italic>generalized state space realization of a polynomial matrix is defined and the mechanism of the \"cancellations\" of \"decoupling zeros at infinity\" is closely examined. The difference between the concepts of<jats:italic>irreducibility<\/jats:italic>and<jats:italic>minimality<\/jats:italic>of generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts of<jats:italic>dynamic<\/jats:italic>and<jats:italic>non-dynamic<\/jats:italic>variables appearing in generalized state space realizations are also examined.<\/jats:p>","DOI":"10.2478\/v10006-009-0007-5","type":"journal-article","created":{"date-parts":[[2009,4,3]],"date-time":"2009-04-03T01:05:55Z","timestamp":1238720755000},"page":"77-88","source":"Crossref","is-referenced-by-count":2,"title":["On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems"],"prefix":"10.61822","volume":"19","author":[{"given":"Antonis-Ioannis","family":"Vardulakis","sequence":"first","affiliation":[]},{"given":"Nicholas","family":"Karampetakis","sequence":"additional","affiliation":[]},{"given":"Efstathios","family":"Antoniou","sequence":"additional","affiliation":[]},{"given":"Evangelia","family":"Tictopoulou","sequence":"additional","affiliation":[]}],"member":"37438","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1080\/00207178108922932","article-title":"Realizations in generalized state-space form for polynomial system matrices and the definitions of poles, zeros and decoupling zeros at infinity","volume":"3","author":"O. 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(1978). <i>Infinite Frequency Behavior in Dynamical Systems<\/i>, Ph. D. thesis, Department of Electrical Engineering, Stanford University."},{"key":"18","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1109\/TAC.1981.1102763","article-title":"A generalized state-space for singular systems","volume":"4","author":"G. 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