On Upper Bounds on Worst-Case H2 Performance for Unstructured Model Perturbations

Abstract

In this note, a sequence of upper bounds is described on the worst-case H2 performance of a given stabilizing controller in the presence of (unstructured) normalized coprime factor perturbations. To obtain such bounds a H2 cost-functional is maximized on sets defined by quadratic constraints. These quadratic constraints are iteratively modified to generate increasingly tighter upper bounds. The maximization required in each step can be carried out through line search and spectral factorization. a numerical example illustrates the range of upper bounds involved.