Copula functions on probabilistic robust analysis

Approaches in probabilistic robust analysis either assume a priori knowledge of the distribution function of the uncertainty, or impose independence and other constrains, for distribution-free results. The scope of this paper is the former. The goal is to ease the task of fitting a joint probability function to a data set. To this end, this paper presents a batch of tools provided by Archimedean copulas for unveiling the structure of dependence of two or more random variables. Then, randomization is used to provide a convenient way to deal with two major open issues in Robust Control: incorporating extra information about the likelihood of uncertainties, and overcoming the computational complexity that prevents many of the robust analysis and design techniques from being eventually carried out.