In this paper we consider single-input single-output (SISO) linear time-invariant systems represented by their ‘meromorphic’ transfer functions, k(s). We assume that k(s) is representative of a given set of uncertainty containing k, and we would like to introduce conditions for determining if a nominal plant exists for k, which would then be used for both analysis and design. It is shown that uncertainty sets representing marginally stable (or unstable) dipoles do not possess nominal plants. Some concluding remarks and suggestions for future research are provided.