In this paper we analyse the problem of continuity of the closed-loop system map as a function of the compensator parameters. Under a suitable parametrization of the compensators we show that a necessary and sufficient condition for the closed-loop systems map to be continuous is given by max (>m, p) ≤ where the plant is a>p×>mplant of degree n. In particular, for single-input single-output plants, the closed-loop systems map is always continuous. The above result is surprising because the inequality is independent of the McMillan degree>qof the compensator. We also analyse the pole placement map and show that it always has points of discontinuity whenever>q> 0.