Fragility problem revisited: overview and reformulation

In a debate paper, Keel and Bhattacharyya have suggested, by means of simple examples taken from the open literature, that optimal and robust controllers can be fragile in the sense that a minute perturbation in the controller parameters can make the closed-loop system unstable. However, is it true that the optimal and robust controllers presented by Keel and Bhattacharyya are actually fragile? It is demonstrated that the particular parametric stability margin used by Keel and Bhattacharyya can be very conservative and to overcome this problem, two non-conservative measures of controller fragility are proposed. In addition, it will be shown that the examples in Keel and Bhattacharyya´s paper are very special and the resulting fragility cannot be linked to the Hinfin optimisation but to non-appropriate Hinfin optimisation criterions and to bad choice of weights.