μ-analysis and synthesis

Abstract

As discussed earlier in the book, the H͚ optimization approach may achieve robust stabilization against unstructured system perturbations and nominal performance requirements. It is, however, possible that by applying appropriate weighting functions some robust performance requirements can be obtained. Satisfactory designs have been reported, in particular when using the H͚ loop-shaping design methods. In order to achieve robust stability and robust performance, design methods based on the structured singular value μ can be used. In this chapter, we first show how a robust performance design specification for a control system with unstructured/structured perturbations can be transformed into a robust stabilization problem with regard to structured perturbation. We then discuss how these design specifications are related to some indications of this new setting, followed by the introduction of two iterative μ-synthesis methods, the D–K iteration and μ–K iteration methods.