Probabilistic enhancement of classical robustness margins: The unirectangularity concept

C. M. Lagoa, P. S. Shcherbakov, B. R. Barmish

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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) developed by Barmish and Lagoa (Math. Control Signals Systems 10 (1997) 203-222), 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. Since such conditions are violated in many practical problems, the objective in this paper is to extend the application of the UP. To this end, by working with a so-called unirectangularity condition, a procedure is implemented for computing probabilities of performance and the associated improvements of deterministic robustness margins. That is, given any robustness radius r0 which is computable via deterministic methods, a probabilistic enhancement of this margin R0(ε)≥r0 with pre-specified level of risk ε>0 is provided. The radius R0(ε) is called a risk-adjusted robustness margin.

Original languageEnglish (US)
Pages (from-to)31-43
Number of pages13
JournalSystems and Control Letters
Issue number1
StatePublished - Aug 25 1998

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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