In this paper, robust multivariable controllers for stable infinite-dimensional systems in the Callier-Desoer algebra (CD-algebra) will be discussed. In particular, the following robust regulation problem will be solved. Given reference and disturbance signals, which are linear combinations of signals of the form t(j) sin(omega(k)t + phi(k)), j greater than or equal to 0, k = 0, ..., n, find a low-order finite-dimensional controller so that the outputs asymptotically track the reference signals, asymptotically reject the disturbance signals, and the dosed-loop system is stable and robust with respect to a class of perturbations in the plant. The proposed controller consists of a positive scaler gain a and certain polynomial matrices K-k(s) for k = 0, ..., n. The main result of the paper shows that the matrices K-k(s) must satisfy certain stability conditions involving the values of the plant transfer function only at the reference and disturbance signal frequencies omega(k) for k = 0, ..., n. Thus, the matrices K-k(s) can be tuned with input-output measurements made from the open-loop plant without knowledge of the plant parameters. The scaler gain epsilon will be tuned experimentally. Because of the internal model principle, the controller has unstable poles on the imaginary axis. When the control loop is dosed, these unstable poles will move Into the left half-plane. The behavior of these pales as a function of the scaler parameter epsilon in the form of a Puiseux series will be given. The results extend our previous results to a larger class of plants and reference and disturbance signals. We also give a generalization of Davison's tuning algorithm, even for finite-dimensional plants. Tn the case of constant reference and disturbance signals, the controller reduces to the well-known multivariable I-controller.