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

The development of controller usually involves two major steps: a design step in which a generalised plant is constructed, followed by a synthesis step in which an optimisation problem is solved for the generalised 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 characterises 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-power gain matrix in the H_∞ loop-shaping design of sampled-data, closed-loop systems