Structure at infinity for discrete time linear periodic systems

The authors introduce a notion of structure at infinity for a special class of linear time-varying systems, namely, discrete-time periodic systems. Also introduced is a sequence of periodic matrices, associated with a given periodic system, which have, in a suitable sense, a sort of Toeplitz structure. The ranks of these matrices are used to define a further r-tuple of integer valued periodic functions which are related by a simple formula to provide an algebraic approach to the notion of structure at infinity