Robust controller design for uncertain time delay systems

Abstract

In this paper we consider robust controller design for uncertain SISO time-delay systems using H ∞ and μ methods. We model the parametric uncertainty with a nominal model plus multiplicative uncertainty and compare a number of different choices for the weight, including real and complex perturbations. Mean values are usually used in the nominal model to get smaller uncertainty. We propose to model also the nominal time-delay as uncertainty. This leads to a larger uncertainty but a delay-free design method for time-delay systems. Surprisingly, though it has larger uncertainty, this new method is not more conservative. The point here is that μ is a worst case measure. Of most importance is not the uncertainty size but the worst uncertainty. This insight is also helpful to the modelling of other uncertain systems.