Periodic-polynomial interpretation for structural properties of linear periodic discrete-time systems

The structural properties of linear periodic discrete-time systems are analyzed in the periodic polynomial representation. It is shown that the classical polynomial approach for linear time-invariant systems can be extended to periodic systems. New definitions and properties are given in terms of skew polynomial rings and periodic difference algebra. Necessary and sufficient conditions for the characterization of reachability, controllability, observability and reconstructibility are given in this framework.