Frequency-domain analysis of linear periodic operators with application to sampled-data control design

Abstract

The development of controller usually involves two major steps: A design step in which a generalized plant is constructed, followed by a synthesis step in which an optimization problem is solved for the generalized plant. Frequency-domain analysis methods are commonly used in the design step; for example loop-shaping. In this paper we develop a new frequency-domain analysis method for periodic operators. Specifically, we define the average-power gain matrix, which for a periodic operator characterizes the average power of the asymptotic (`steady-state') response to a sinusoidal input of a single frequency. To illustrate an application of the new analysis method we show how to use the average..