On the probabilistic characterization of model uncertainty and robustness

This paper considers the probabilistic characterization of model uncertainties and stability robustness on the Nyquist diagram. For any given ε>0, any frequency ω, we describe the boundary of a domain D_ε,ω such that the frequency response of an uncertain plant at that frequency ω is guaranteed in the domain with a probability of at least 1-ε where ε⩽ε is a function of ε and frequency ω and a upper bound of ε can be estimated easily. Then, by analyzing the evolution of the boundary of D_ε,ω as a function of the frequency ω, a combined curve C is constructed such that it includes the boundary of a domain D_ε covering the Nyquist plot with a probability of at least 1-ε for a range of frequencies