TABLE OF CONTENTS We have seen in the previous section how a parametric confidence region 
, guaranteed to contain the unknown true system G 0 with a chosen probability p, could be built using prediction-error identification. In this section, we describe tools for using the uncertainty region 
in a robust control framework. These tools are, respectively, a control-oriented measure of the size of a generic prediction-error uncertainty set 
of the form (5.27) (Subsection 5.3.1), controller validation tools for stability (Subsection 5.3.2) and controller validation tools for performance (Subsection 5.3.3).
The uncertainty region 
of (5.27) depends very much on the experimental conditions used for the validation experiment: open-loop or closed-loop setup, choice of signal spectra, etc. Thus, different validation experiments yield different uncertainty regions 
, each containing the true G 0 with probability p. It is therefore useful to possess a measure of quality of a model set 
that is connected to the size of a controller set that stabilises all models in 
. Such a measure is the worst-case ?- gap and its frequency-by-frequency counterpart, the worst-case chordal distance. They are extensions of Vinnicombe's ?-gap and chordal distance between two transfer functions and are defined as follows.
(WORST-CASE CHORDAL distance) The worst-case chordal distance at frequency us between a nominal system G nom and all systems in...
