A pitfall in some of the robust stability literature

Firstly, it is shown that the robustness margin is not necessarily continuous with respect to the problem data. This discontinuity phenomenon is seen to be independent of the computational algorithm used to find the robustness margin, i.e. the authors raise the possibility that the universally accepted definition of the robustness margin is in a sense defective. Matters are further complicated by the fact that at the point of discontinuity, the robustness margin may be much smaller than at neighboring points. This may lead to potentially deceptive conclusions. Secondly, it is demonstrated that there may be severe consequences of the discontinuity phenomenon when numerical computation of the margin is attempted