In a recent paper, Keel and Bhattacharyya suggest, by means of simple examples taken from the literature, that H<FONT FACE=Symbol>¥</FONT> robust controllers can be fragile in the sense that a minute perturbation in the controller parameters can make the closed-loop system unstable. Subsequent works have related this problem to controller implementation and suggested that modern H<FONT FACE=Symbol>¥</FONT> design methodology (e.g. McFarlane-Glover) where more than one design criteria is considered should be used. However, is it true that robust controllers, designed for the simple optimization criteria presented by Keel and Bhattacharyya, are necessarily fragile? In this paper this question is answered and it will be shown that the fragility problem can not be associated to H<FONT FACE=Symbol>¥</FONT> optimization, since it is possible to find controllers that are non-fragile and also lead to a cost value close to the optimal value obtained in the H<FONT FACE=Symbol>¥</FONT> optimization problem.
H<FONT FACE=Symbol>¥</FONT> control; robust control; fragility; linear systems
