Abstract
Given an input-output periodic application, we prove that a periodic realization is minimal if and only if it is reachable and observable. We define the block Hankel matrix associated with the input-output periodic application, and we obtain the dimension of the minimal realization by means of the rank of it. This is the extension of the well-known result for the invariant case. Furthermore, we study similar periodic systems which are basic for getting minimal periodic realizations.
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