Probabilistic enhancement of classical robustness margins: the unirectangularity concept

The focal point of this paper is a control system subjected to parametric uncertainty. Motivated by the newly emerging theory of probabilistic robustness, the risk of performance violation is assessed with uncertainty bounds which exceed classical deterministic margins. For a wide class of problems, the uniformity principle (UP) makes it possible to estimate the probability of performance satisfaction with almost no a priori statistical information about the uncertainty. The application of the UP is, however, limited to problems satisfying certain convexity and symmetricity conditions. This paper extends the application of the UP by working with a so-called unirectangularity condition.