{\it Robustness margin} of a given system with fixed values of parameters $p_1,...,p_n$ is, crudely speaking, the largest width $\Delta$ of uncertainty intervals, for which every system with parameters $p'_i\in [p_i-\Delta,p_i+\Delta]$ is still stable. In this paper, it is shown that the dependence of the robustness margin on the values of the parameters can be discontinuous. Near this discontinuity, computing the exact value of the robustness margin can be extremely difficult.

This mathematical result thus explains later results by Rohn et al. that computing the robustness margin is computationally intractable (NP-hard).