Robust performance and stability for simultaneous parameter and high frequency uncertainty

The authors develop bounds for robust stability of feedback systems subject to a class of uncertainty that includes simultaneous unstructured and parametric uncertainties. An approach that can analyze such systems and provide synthesis criteria for them is elaborated. The robust performance design problem with both types of uncertainties is formulated using the structured singular value, which can be used to provide insight into the mechanisms through which the simultaneous uncertainties affect the system performance. The structured singular value formulation is then used to study the interaction of the unstructured uncertainty and parameter uncertainty in a simplified system. The analysis and synthesis techniques described here are applied to a model of a gallium arsenide crystal growth process