Low gain tracking for well-posed systems

In this paper we solve a stabilization and tracking problem for linear systems, using a low gain controller suggested by the internal model principle. These results are a partial extension of results by Hämäläinen and Pohjolainen. In their results the plant is required to have a transfer function in the Callier-Desoer algebra, while in this paper we only require the system to be well-posed. The conditions for a transfer function to be well-posed are sufficiently unrestrictive to be verifiable for many partial differential equations in more than one space variable. In this paper we apply our results to the problem of rejecting external noise in a model for structure/acoustics interactions.