Abstract
Reachability, observability, controllability and reconstructibibty of linear Periodic Discrete-Time (LPDT) systems are defined here in the context of module theory. We describe after, the two possible structures of the generalized state space representation according to the LPDT system to be regular or descrptor. The no-equivalence between canonical and minimal realization for LPDT (and consequently for discrete time-varying) systems is clearly proved. Periodic structural invariants of LPDT system (such as poles, zeros…) and their link with invariants factors (when they exist) of periodic matrices is sketched in the appendix.
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