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. Speciically, we deene 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 1 loop-shaping design of sampled-data, closed-loop systems.