PROBABILISTIC μ UPPER BOUND USING LINEAR CUTS

摘要

As a direct extension of the structured singular value μ framework from the worst-case to the probabilistic robustness analysis, probabilistic μ defines a probability measure of performance assuming some distribution on the uncertainty. Exactcomputation of probabilistic μ is intractable. Standard branch and bound methods with axially aligned cuts had been applied to compute a hard upper bound for probabilistic μ, which failed to give satisfactory solutions. This paper explores the use oflinear cuts in the upper bound computation, which involves the construction of an implicit system. The bounds achieved are exact for rank-one problems. The algorithm has also been tested on random matrices and the results will be compared to thoseobtained by the standard B&B algorithm.