On the Robustness of Sampled-Data Systems to Uncertainty in Continuous-Time Delays

Abstract

In this technical 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 misleading. Namely, we show that there are systems, which are destabilized by small continuous-time delays despite being delay-independent stable with respect to “integer” delays (this phenomenon has no continuous-time counterpart). 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> problem. Toward this end, a novel nominal model for the uncertain delay is put forward. It yields a tighter unstructured uncertainty covering than in the existing approaches, thus having a potential to reduce the conservatism of the method. This might be advantageous in the pure continuous-time case as well.