Representation of uncertain time delays in the H_∞framework

Abstract

Abstract How to represent an uncertain time delay in a form suitable for robust control in terms of the H∞-norm and the structured singular value (µ) is discussed. To use µ-synthesis the uncertain delay has to be approximated to yield a proper rational interconnection matrix M(s) and a purely complex perturbation matrix? (s). The parametric average of the delay is usually included in the nominal model, while the uncertain perturbation covers variation around the average delay. It is proposed to model the nominal time delay as uncertainty, i.e. using a larger uncertainty set. This yields a delay-free nominal model, which simplifies the controller synthesis. For the cases studied the delay free nominal model does not yield a more conservative design than the average delay model, despite its larger uncertainty set.