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This paper addresses the issues of conservativeness and computationalcomplexity of probabilistic robustness analysis. We solve both issues bydefining a new sampling strategy and robustness measure. The new measure isshown to be much less conservative than the existing one. The new samplingstrategy enables the definition of efficient hierarchical sample reusealgorithms that reduce significantly the computational complexity and make itindependent of the dimension of the uncertainty space. Moreover, we show thatthere exists a one to one correspondence between the new and the existingrobustness measures and provide a computationally simple algorithm to deriveone from the other.

A Statistical Theory for the Analysis of Uncertain Systems