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

• Published in: Proceedings of the 36th IEEE Conference on Decision and Control Vol. 5; pp. 4318 - 4323 vol.5
• Main Authors: Cantoni, M.W., Glover, K.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1997
• Subjects: Equations; Frequency dependence; Frequency domain analysis; Frequency response; Sampling methods; Steady-state; Symmetric matrices
• ISBN: 0780341872; 9780780341876
• ISSN: 0191-2216
• DOI: 10.1109/CDC.1997.649525

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/sub /spl infin// loop-shaping design of sampled-data, closed-loop systems.