A measure of robust stability for an identified set of parametrized transfer functions

In this paper, we define a measure of robustness for a set of parameterized transfer functions as delivered by classical prediction error identification and that contains the true system at a prescribed probability level. This measure of robustness is the worst case Vinnicombe distance between the model and the plants in the uncertainty region. We show how it can be computed exactly using LMI-based optimization. In addition, we show that this measure is directly connected to the size of the set of controllers that are guaranteed to stabilize all plants in the uncertainty region, i.e., the smaller the worst case Vinnicombe distance for an uncertainty region, the larger the set of model-based controllers that are guaranteed to stabilize all systems in this uncertainty region.