Probabilistic μ for rank-one and perturbed rank-one matrices

The structured singular value μ has been widely studied for uncertain dynamical systems. Recently a great attention is paid to the probabilistic μ problem. Instead of computing the conservative worst-case μ we are interested in the probabilistic distribution of μ; given a probability distribution on the set of uncertainties. Traditionally this problem is solved by Monte Carlo algorithms. In this paper we propose analytic methods to compute the probabilistic μ for rank-one and perturbed rank-one matrices. We expect that these results will provide an algorithm that is not as computationally expensive as the linear cut algorithm in [1].