Improved bounds computation for probabilistic μ

Probabilistic μ is a direct extension of the structured singular value μ from the worst-case robustness analysis to the probabilistic framework. Its computation involves approximating the level surface of some performance function in the parameter space, which is more complex than the worst-case μ computation. In particular, providing a sufficiently tight upper bound in the tail of the distribution is extremely difficult. The approach presented in this paper is a mixture of the linear cut and the branch and bound algorithms. It greatly improves the probabilistic μ upper bound on average, which is shown through numerical experiments. The tightness of the bounds can be tested by comparing the hard upper bounds with the soft bounds provided by Monte-Carlo simulations