SVD controllers for H2-, H∞-, and μ-optimal control

For plants where the directionality is independent of frequency, the singular value decomposition (SVD) is used to decouple the system into nominally independent subsystems of lower dimension. In H₂- and H_∞-optimal control, the controller synthesis can thereafter be performed for each of these subsystems independently, and the resulting overall SVD controller will be optimal. In H_∞-optimal control the resulting controller is also super-optimal. For robust control in terms of the structured singular value, μ, the use of the SVD decomposition can lead to significant simplification in controller synthesis, but the optimality of the SVD controller will depend on the structure of the uncertainty. The results are applied to the ill-conditioned distillation case study of Skogestad et al. (1988), where it is shown that an SVD controller is μ-optimal for the case of unstructured input uncertainty.