A Frequency Domain Approach to Controller Design for Linear, Time-Invariant, Infinite-Dimensional Systems

We present a new approach to frequency domain controller design for innite dimensional systems. The chapter is organized around two examples: The rst, an introductory example, is used to demonstrate how innite dimensional systems arise in control theory and some of the features that distinguish them from nite dimensional systems. This example also provides an opportunity to introduce the basic algebraic structure on which our approach is based. The second example is used to motivate the bulk of the work in the chapter which specializes the algebraic approach to the function space H1. The advantage of this specialization is that it allows the introduction of powerful, general, analytic methods for constructing solutions to the algebraic equations that underly controller design. Finally we present the algebraic theory required to extend the design approach to multi-input, multi-output systems.