Output stabilization via pole placement of discrete-time linear periodic systems

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Abstract
The output stabilization problem for discrete-time linear periodic systems is solved. Both the state-feedback control law and the state-predictor are based on a suitable time-invariant state-sampled reformulation associated with a periodic system. Preliminary concepts of periodic system theory are briefly recalled. In particular, the structural properties of a linear discrete-time periodic system are properly related to those of a time-invariant system associated with it. By resorting to such a time-invariant reformulation, the output stabilization problem via pole placement is solved. The stabilizing controller is constituted by a control law and an asymptotic state predictor, both of which are shown to be periodic.