Model reduction via the largest robust stability radius

A sharp bound is derived for the difference between the largest robust stability radii of any two systems. This bound implies the continuity of the largest robust stability radius as a function of the systems. Then this result is applied to model reduction and an estimate obtained by McFarlane, Glover and Vidyasagar (1990) is improved in this note. Finally, an example is given showing approximation in the gap metric with different number of unstable poles. This implies that the optimally robust controllers designed according to lower order models with less unstable poles will stabilize the original higher order systems