Radially truncated uniform distributions for probabilistic robustness of control systems

In this paper, a new approach to probabilistic robustness is developed in the context of unstructured uncertainty. For a control system with a bound on the uncertain quantities of interest, the probabilistic robustness margin R_max(ε) describes the radius of tolerable uncertainty as a function of the risk level 0≤ε≤1. In addition, associated with the performance risk probability p = ε, the computed radius R_max(ε) is guaranteed for a large class of radially symmetric nonincreasing density functions. In other words, the results are distribution-free in the sense that the user does not need to have a detailed description of the statistics of the uncertainty other than a radial bound.