Branch and bound algorithm for the robustness analysis of uncertain systems*

Computing the worst-case spectral abscissa of a system with uncertain parameters allows to decide whether it is robustly stable in a given parameter range. Since this problem is NP-hard, we use a heuristic local optimization method based on a bundle trust-region strategy to compute good lower bounds. Then we employ branch-and-bound to certify the global maximum. A specific frequency sweeping technique is used to accelerate the global optimization.