H-INFINITY OPTIMAL AND SUBOPTIMAL CONTROLLERS FOR INFINITE-DIMENSIONAL SISO PLANTS

This paper presents a simple formula for H(infinity) 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 n1 + l - 1 (n1 + l in the suboptimal case), where l is the number of unstable poles of the plant and n1 is the order of the sensitivity weighting function. There are 2(n1 + l) (2(n1 + 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.