On the structure of H∞ controllers

In this paper we study the structure of two block H^∞ controllers, for unstable SISO distributed plants. The authors previously showed (1993) that all H^∞ controllers can be expressed in terms of (i) inner and outer parts of the plant, (ii) a finite dimensional spectral factor obtained from the weighting functions, and (iii) a rational function satisfying certain interpolation conditions. For a class of infinite dimensional plants, we show that if we have “full information” about external signals, then the controller can be implemented using rational transfer functions. The problem of finding a stable (i.e. strongly stabilizing) H ^∞ controller is also investigated here. By studying this controller structure, a procedure for obtaining finite dimensional H^∞ suboptimal controllers is also derived