Probabilistic Enhancement of Classical Robustness Margins: A Class of Nonsymmetric Distributions

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In this note, we address the problem of risk assessment when the robustness margin is exceeded, without a priori knowledge of the distribution of the uncertainty. The only assumption is that the distribution belongs to a given class. In contrast to previous work, this class contains both symmetric and nonsymmetric distributions. We prove that the assessment of risk can be done using only a subset of the admissible distributions. Also, if the set of uncertainties that verify the specifications is convex, it is proven that risk assessment can be done using only a finite subset of the class. Finally, a way of estimating risk is provided for the nonconvex case.

Original languageEnglish (US)
Pages (from-to)1990-1994
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number11
StatePublished - Nov 2003

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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