Robust performance synthesis for systems with positive-real uncertainty and an extension to the negative-imaginary case

This paper addresses the robust performance synthesis problem for systems with positive-real or negative-imaginary uncertainty. The conventional robust performance design methods are mostly based on the gain information of uncertainty, which is not suitable for uncertainties characterized by the phase information. The approach taken here is based on the input-output relation of systems in the frequency-domain, which enables a less conservative yet numerically tractable solution to the robust performance synthesis. The effectiveness is validated through a detailed case study on the head positioning control of hard disk drives. The results and comparison demonstrate that the proposed method can achieve a much higher robust performance than existing methods.