New tools for computing tight bounds on the real structured singular value

New tools are presented for the computation of tight lower bounds on the structured singular value μ, for high-order plants subject to purely real parametric uncertainty. The first approach uses the μ-sensitivity function to systematically reduce the order of the real uncertainty matrix, so that exponential time lower bound algorithms can be applied. The second approach formulates the search for a worst-case real destabilizing perturbation as a constrained nonlinear optimization problem. Both approaches are applied to the problem of analyzing the stability robustness properties of an integrated flight and propulsion control system for an experimental vertical/short takeoff and landing aircraft configuration. Currently available software tools for calculating lower bounds on real μ fail for this problem, whereas both new approaches deliver tight bounds over the frequency range of interest.