New Tools for Computing Tight Bounds on the Real Structured Singular Value

Abstract

New tools are presented for the computation of tight lower bounds on the structured singular value π, for highorder plants subject to purely real parametric uncertainty. The e rst approach uses the π-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 nonlinearoptimization problem.Both approachesareapplied to theproblem ofanalyzing thestability robustness properties of an integrated e ight and propulsion control system for an experimental vertical/short takeoff and landing aircraft cone guration. Currently available software tools for calculating lower bounds on real π fail for this problem, whereas both new approaches deliver tight bounds over the frequency range of interest.