New algorithms for upper and lower bounds on the mixed/real structured singular value

New algorithms are presented for the computation of good upper and lower bounds on the structured singular value μ, for high order plants subject to purely real or mixed real/complex uncertainty. A geometric form of the Hahn-Banach theorem is used to develop an algorithm for computing an upper bound on μ, involving a linear program and a symmetric eigenvalue problem at each iteration. A proof of convergence to a convex upper bound on μ is presented. The new lower bound algorithm formulates the search for a worst-case real (or mixed) destabilising perturbation as a constrained non-linear optimisation problem. The new algorithms are compared with currently available software tools for computing μ on a large scale stability robustness analysis problem for an experimental V/STOL aircraft configuration.