Structure and Parametrization of Periodic Linear Systems U. Helmke ∗ Department of Mathematics, University of W¨ urzburg D-97074 W¨ urzburg, Germany E. I. Verriest † School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, GA 30332-0250 January 4, 2011 Abstract In this paper the beginnings of a structure theory for discrete–time periodic linear systems are developed. Canonical forms for state space realizations are described, structural in- variants and their combinatorics are studied and geometric aspects of the parametrization of periodic systems are treated. Keywords: Discrete–time periodic systems, Canonical forms, Invariants, Parametriza- tion, Topology. * Research partially supported by a grant from the German-Israeli Foundation GIF I-526-034.6/97 as well as through HE 1858/12-1 within DFG Priority Program 1305 † Corresponding author: Phone: +1 404 894 2949; Fax: +1 404 894 5935; e-mail: erik.verriest@ece.gatech.edu. 1