Randomized algorithms for probabilistic robustness with structured uncertainty

In this paper, randomized algorithms for stability and performance of linear time invariant uncertain systems described by a general M-Δ configuration are studied. On the contrary of the worst-case approach, which is often not tractable in the NP-hardness sense, this problem turns out to be solvable in a probabilistic setting. In particular, efficient polynomial-time algorithms for uncertainty structures Δ consisting of an arbitrary number of full complex blocks and uncertain parameters, real or complex and possibly repeated, are developed