This thesis presents a new approach to frequency domain design of robust controllers for distributed parameter systems. The central idea is to use techniques from complex analysis, that were developed for the solution of the Corona Problem, for the solution to the Bezout equation that arises in the parameterization of stable feedback controllers. An algebraic reformulation of the Bezout equation allows the solution to be computed from the solution of an auxiliary equation with a Carleson measure as the inhomogeneous term.

We first show how the Bezout equation arises in the problem of feedback controller design, then we present techniques that are used for its solution. An example is given in which the solution to a Bezout equation derived from an unstable plant with a delay is calculated. Finally this example is extended to show how the techniques developed for the Bezout equation may be used to calculate a sub-optimal solution to the Nehari Problem for a single-input single output system.