On the sample complexity of randomized approaches to the analysis and design under uncertainty

In this paper, we study the sample complexity of probabilistic methods for control of uncertain systems. In particular, we show the role of the binomial distribution for some problems involving analysis and design of robust controllers with finite families. We also address the particular case in which the design problem can be formulated as an uncertain convex optimization problem. The results of the paper provide simple explicit sample bounds to guarantee that the obtained solutions meet some pre-specified probabilistic specifications.