Structured singular value controller synthesis using constant D-scales without D-K iteration

Structured singular value synthesis allows the design of controllers that are robust with respect to multiple block uncertainty. This type of design process commonly relies on "D-K iteration" and curve fitting. In particular, the optimal D-scales and the controller are iteratively optimized. Since the D-scales are optimized over frequency, they must be curve fitted with rational transfer functions before the controller is optimized. This curve fitting can be difficult and lead to suboptimal designs. This paper presents a structured singular value process that allows the D-scales to be constrained, to be constant and simultaneously optimizes the D-scales and the controller K. The approach relies on recent results on mixed-norm H₂/H controller synthesis and also enables the direct design of reduced-order controllers.