On quantifying tolerable closed-loop uncertainty in frequency domain

Given a linear plant and a feedback controller it is natural to ask: How much uncertainty can be tolerated by the closed-loop while achieving a specified level of performance? In this paper, a characterization of this question is formulated in terms of a constrained optimization problem; the cost reflects the size of non-constant weights used to quantify system uncertainty across frequency and the constraint is a structured singular value characterization of the required level of robust performance. In the case of unstructured uncertainty the problem can be solved via a family of problems that are convex pointwise in frequency. An iterative algorithm is developed for the case of structured uncertainty.