The significance of certain basic stability concepts for feedback systems are discussed in the light of the recent interest in non-fragile controller design. It is shown that certain standard controller representations can have vanishing stability margins against controller coefficient perturbations for control problems defined on the doubly-infinite time axis. Furthermore, it is demonstrated via control examples, on the standard singly-infinite time axis, that in general it does not suffice to consider robustness against plant and controller perturbations in terms of specifications on the sensitivity and complementary sensitivity function only.