A New Algorithm for the Real Structured Singular Value

A new algorithm is presented for computing a tight lower bound for Doyle\´s Structured Singular Value (SSV) in the case of real uncorrelated parameter uncertainty. The algorithm has several desirable features: it consists entirely of simple matrix algebra operations; it iterates on only one variable; and it returns the actual values of the "worst-case" parameters, not just their size. Unlike other algorithms for the real SSV, it does not require the computing of convex hulls or other difficult geometric constructs. This lower bound is conjectured to be exactly equal to the real SSV for a wide class of matrices. The new algorithm has wide applications for control system design; several types of control system robustness tests are identified. A numerical example is given for a 6 by 6 complex matrix.