A Sharp Estimate for the Probability of Stability for Polynomials With Multilinear Uncertainty Structure

This paper addresses the probability of stability for uncertain polynomials that have multilinear functions of real parameters as coefficients. We obtain an estimate for the probability of stability with respect to a class of admissible distributions. This estimate is ldquosharprdquo in the following sense: one obtains a probability of stability of unity when the bounds on the hypercube uncertainty bounding set are below the deterministic robustness radius obtained with the well-known mapping theorem.