A worst-case estimate of stability probability for polynomials with multilinear uncertainty structure

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Distributionally robust gain analysis for systems containing complex uncertainty

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The Uniformity Principle: A New Tool for Probabilistic Robustness Analysis

This paper provides a new mathematical framework for analysis of control systems which are operated with admissible values of uncertain parameters which exceed the bounds specified by classical robustness theory. In such a case, it is important to quantify the tradeoffs between risk of performance degradation and increased tolerance of uncertainty. If a large increase in the uncertainty bound can be established, an acceptably small risk may often be justified. Since robustness problem formulations do not include statistical descriptions of the uncertainty, the question arises whether it is possible to provide such assurances in a "distribution-free" manner. In other words, if F denotes a class of admissible probability distributions for the uncertainty X, we seek some worstcase f 2 F having the following property: The probability of performance satisfaction under f is smaller than the probability under any other f 2 F . Said another way, f provides the best possible guarantee..