Tradeoffs for multitrate controller design and exact comparisons with single-rate control

Linear controller design as a convex optimization problem is addressed. For a simple plant, with two robustness measures and a root mean square noise merit figure, C. Barratt and S. Boyd (ibid., vol.9, no.1, pp. 46-51, Jan 1989) used convex optimization to compute performance tradeoff curves showing the best performance achievable with any linear single-rate digital controller. Linear multirate performance tradeoff curves are given for the same simple plant using convex optimization and the theory of multirate lifts. The performance differences that can be obtained with multirate sampling are illustrated, making a simple exact comparison between multirate and single-rate sampling possible.<>