H∞ controller design for pure delay and other distributed systems

In this paper we consider the design of a rational stabilizing controller for a weighted two-block H problem with a distributed plant, with emphasis on the case of a pure delay plant and first order weights. The optimal controller for such a problem is, in general, distributed and requires rational approximation. We propose a simple suboptimal design procedure, which is based on Pade approximation with two crucial modifications: (i) high frequency performance is modified using a first-order approximated inverse; (ii) an additional one-point interpolation condition is imposed to restore stability at a critical imaginary unstable pole. The design trade-offs are discussed, with an example.