An iterative method for propagation of probability distributions in feedback systems

Efficient propagation of probability distributions in feedback systems is central to a decomposition based approach for uncertainty propagation in complex, interconnected systems. In this note, we propose an iterative method for static feedback systems to obtain the probability density of the output from that of the input. We prove the convergence of the proposed method under the assumption that the loop operator is contractive. It is shown, based on the results from the theory iterated random functions, that the method extends to the case when additional parametric uncertainty is present within the loop.