Minimal complexity control law synthesis, part 2: problem solution via H2/H∞ optimal static output feedback

In part 1 of this two-part paper [1] it was shown that a large class of fixed-structure control laws can be recast as static output feedback controllers for a suitably modified plant. Accordingly, we develop here a comprehensive theory for designing static output feedback controllers. Our results go beyond earlier work by addressing both H2 and H_∞ performance criteria and by accounting fully for all of the singularities in the problem formulation. The results are applied to the fixed-order problem (FoP) [1] to obtain a major unification of prior results, namely: the Bernstein-Haddad H₂/H_∞ fixed-order dynamic compensator theory, the Glover-Doyle full-order H_∞ dynamic compensator theory, the Hyland-Bernstein H₂ fixed-order dynamic compensator (optimal projection) theory, and the classical LQG theory.