Wiener-Hopf Control of Stable Infinite Dimensional Systems

This paper takes an Approximate/Design approach to the problem of designing near optimal finite dimensional compensators for scalar infinite dimensional plants. The criteria used to determine optimality are standard H² (Wiener-Hopf) weighted sensitivity and mixed-sensitivity measures. More specifically, it is shown that given a "suitable" finite dimensional approximant for an infinite dimensional plant, one can solve a "natural" finite dimensional problem in order to obtain a near optimal finite dimensional compensator. Moreover, very weak conditions are presented to indicate what a "suitable" approximant is. In addition, we show that the optimal performance can be computed by solving a sequence of simple finite dimensional Lyapunov equations. Finally, guarantees are given on the "loop shapes" of the actual designs with respect to the optimal "loop shapes".