Some new properties of the structured singular value

J.C. Doyle et al. (1982) have shown that a necessary and sufficient condition for robust stability or robust performance in the H/sup infinity /-frame work may be formulated as a bound on the structured singular value ( mu ) of a specific matrix M which includes information on the system model, the controller, the model uncertainty, and the performance specifications. Often it is desirable to express the robust stability and performance conditions as norm bounds on transfer matrices (T) which are of direct interest to the engineer, e.g. sensitivity or complementary sensitivity. The present paper shows how to derive bounds on sigma (T) from bounds on mu (M).<>