Improved Robust Performance Design for Passive Uncertain Systems-Active Use of the Uncertainty Phase and Gain

In the robust performance design, the celebrated $\mu$-synthesis provides a reputed tool for systems with norm-bounded uncertainty. However, such small-gain methods inevitably limit the achievable robust performance when the dynamic uncertainty is not characterized by its gain bound. To achieve a high robust performance for systems with positive real (PR) uncertainty, an output strict passivity (OSP) approach is proposed recently which makes use of the positive realness and the maximum gain information of the uncertainty. Aiming at an even higher robust performance, this article proposes a novel model for PR uncertainties which captures the frequency-dependent gain bound, and establishes the corresponding design theory to actively utilize both gain and phase bounds of the uncertainty in the robust performance design. A case study reveals that the new uncertainty model alone yields a substantial improvement over the OSP method in performance even under the same design setup. Moreover, the best tuned controller outperforms the OSP controller.