On the robustness of sampled-data systems to uncertainty in continuous-time delays

In this note, we consider the robust stability of sampled-data systems with respect to continuous-time delay. We argue that many results in the literature implicitly assume that the delay is a multiple of the sampling period. We demonstrate that this approach might be arbitrarily misleading. Namely, we construct an example, which is delay-independent stable for such “integer” delays, whereas becomes unstable under an arbitrarily small continuous-time delay. We also propose a robustness analysis procedure based on embedding continuous-time delays into unstructured analog uncertainty with the subsequent reduction of the problem to a standard sampled-data H^∞ problem. Toward this end, a novel covering weight is proposed, which can potentially reduce the conservatism of the method. This weight might be advantageous in the pure continuous-time case as well.