Frequency domain design trade-offs for linear periodic feedback systems

The purpose of this paper is to analyse inherent design limitations associated with systems that are linear and periodically time-varying. The contributions of the paper are (i) to relate frequency domain raising methods from signal processing literature to time-domain lifting used in control literature, and (ii) to develop extensions of the Poisson sensitivity and complementary sensitivity integral constraints. In particular, it is shown that there is generally an additional cost associated with having a time invariant target closed loop for a periodic open loop plant. It is also shown that design limitations due to unstable poles and/or non-minimum phase zeros of a discrete linear time-invariant plant remain even ifa periodic time-varying controller is used. As a consequence, the utility of periodic control in circumventing design limitations is questioned.