Approximate Tracking and Disturbance Rejection for Stable Infinite-Dimensional Systems Using Sampled-Data Low-Gain Control

In this paper we solve tracking and disturbance rejection problems for stable infinite-dimensional systems using a simple low-gain controller suggested by the internal model principle. For stable discrete-time systems, it is shown that the application of a low-gain controller (depending on only one gain parameter) leads to a stable closed-loop system which asymptotically tracks reference signals r of the form r(k)=∑ⱼ₌₁N λⱼᵏ\, rⱼ, where rⱼᵖ and λⱼ with |λⱼ|=1 for j=1,…,N. The closed-loop system also rejects disturbance signals which are asymptotically of this form. The discrete-time result is used to derive results on approximate tracking and disturbance rejection for a large class of infinite-dimensional sampled-data feedback systems, with reference signals which are finite sums of sinusoids, and disturbance signals which are asymptotic to finite sums of sinusoids. The results are given for both input-output systems and state-space systems.