Time-Varying z-Transform for the Analysis of Discrete-Time Linear Time Periodic Systems

This article deals with a new representation of linear discrete-time periodic systems. This representation, based on the time-varying z-transform, turns out to be highly efficient in the field of automatic control, when an appropriate choice of the sampling period is made. This representation permits to extend many well-known theorems, in particular, the initial- and final-value theorems, to the case of these systems and to predict the presence of limit cycles. Finally, this representation can be used to establish an extension of the Nyquist criterion to the feedback discrete-time periodic systems.

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