The uniform distribution: A rigorous justification for its use in robustness analysis
type: Item
instance of: scholarly article
title: The uniform distribution: A rigorous justification for its use in robustness analysis
zbMATH Open document ID: 0892.93042
DOI: 10.1007/BF01211503
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1998-01-26T00:00:00Z
review text: Consider a control system which is operated with admissible values of uncertain parameters which exceed the bounds specified by classical robustness theory. Then the tradeoffs between risk of performance degradation and increased tolerance of uncertainty should be quantified. The main results are provided in the context of robust stability analysis problems involving real parametric uncertainty. Two basic questions are addressed here: i) ``When can one ``safely'' operate with uncertain parameter bounds which exceed the stability margins given by classical robustness theory?'' and ``Can the assessment of risk be made in a ``distribution-free'' way?'' Under some assumptions given in the paper, the main results described here provide a rationale for use of the uniform distribution when little or no a priori statistical information about the uncertain parameters is available.
Mathematics Subject Classification ID: 93C41
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93D09
zbMATH DE Number: 1109559
zbMATH Keywords: robustness theory
zbMATH Keywords: risk of performance degradation
zbMATH Keywords: tolerance of uncertainty
zbMATH Keywords: robust stability
zbMATH Keywords: parametric uncertainty
zbMATH Keywords: uniform distribution
author: B. Ross Barmish
author: Constantino M. Lagoa
reviewed by: Kurt Marti
MaRDI profile type: Publication
cites work: Q4196736
cites work: Root locations of an entire polytope of polynomials: It suffices to check the edges
cites work: Q5485394
cites work: Robust Statistics
cites work: Stochastic robustness of linear time-invariant control systems
cites work: A Monte Carlo approach to the analysis of control system robustness
cites work: Geometry. I, II. Transl. from the French by M. Cole and S. Levy
cites work: Convex Analysis
full work available at URL: https://doi.org/10.1007/bf01211503
OpenAlex ID: W2163146959
description: scientific article; zbMATH DE number 1109559