Bounds on the three-block structured singular value

The structured singular value is a useful tool with which to analyze stability and performance robustness of feedback systems with respect to several sources of modelling uncertainty. To use the structured singular value in design, it is necessary to understand the relation between its size and the plant and compensator of the system. In this note we present lower and upper bounds upon the structured singular value for two or three sources of uncertainty. These bounds are useful in that they are easy to compute and, as analyses to be presented elsewhere show, they may be analyzed to provide insights useful in design.