A less conservative robust control method for a class of nonpassive uncertain systems

In robust control problems, how to elicit and utilize the uncertainty information is the key in achieving a good robust performance. For passive uncertainties, the phase bound plays a fundamental role. For nonpassive uncertainties, the gain bound is used up to date. The former leads to the passivity approach and the later to the small-gain approach. A recently developed bounded positive real model succeeded in extracting both the phase and the gain information from passive uncertainties. However, it is still not known how to model the phase bound of a nonpassive uncertainty. Aiming at achieving an even higher performance for nonpassive uncertain systems, this article proposes a new model together with a modeling procedure for a class of nonpassive uncertainties. This model well captures both the gain and the phase features of the nonpassive uncertainty. Further, a numerically tractable design method is developed by extending the passivity method. The advantage of the proposed method is demonstrated through a real-world case study.