Robust Performance Design for Systems With Output Strictly Passive Uncertainty

In the robust control of systems with dynamic uncertainty, there are mainly two methodologies: one based on the gain bound of uncertainty and the other based on the phase bound. The well-known small-gain approach belongs to the former and is able to conduct nonconservative robust performance design by using $\mu$ -synthesis. Meanwhile, the study on the latter case is still under way, and only a positive-real method was proposed by the authors recently to handle the robust performance synthesis. This paper aims at improving the positive-real method. The key idea is to model a passive uncertainty not only by its phase bound but also utilizing its largest gain. This is achieved by applying the notion of output strict passivity well known in nonlinear control. Furthermore, the negative-imaginary uncertainty can be treated in this framework more naturally. A case study on a vibration system validates the advantage of the present method.