Analysis of H2 and H∞ performance of discrete periodically time-varying controllers

Abstract This paper presents analysis of the H 2 and H ∞ performance of discrete linear periodically time-varying controllers for control of linear time-invariant plants. Using a frequency-domain lifting approach, the analysis distinguishes periodically time-varying control from time-invariant control to show that the multiple transfer channels of the system time-varying dynamics amplify the overall system gain. Such a result can provide deeper insights into the system time-varying mechanism and clarify how the time-varying dynamics acts and degrades the system performance. Quantitatively, the paper presents necessary and sufficient conditions under which a linear time-invariant controller can be found to provide strictly better control than periodically time-varying controllers.

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