H/sup ∞/ optimal and suboptimal controllers for infinite dimensional SISO plants

Abstract

This paper presents a simple formula for H/sup /spl infin// optimal and suboptimal controllers for unstable SISO distributed plants, with rational weighting functions. The controller is 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. Under certain genericity assumptions, this rational function is of dimension less than or equal to n/sub 1/+l-1 (n/sub 1/+l in the suboptimal case), where l is the number of unstable poles of the plant and n/sub 1/ is the order of the sensitivity weighting function. There are 2(n/sub 1/+l) (2(n/sub 1/+l+1) in the suboptimal case) linear equations, which determine this rational function. These linear equations can be written directly from the structure of the controller. >