Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis

DOI10.1007/BF02741890zbMath0921.93007OpenAlexW3162505434MaRDI QIDQ1272556

Roberto Tempo, Fu, Minyue, Er-wei Bai

Publication date: 3 January 1999

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02741890

zbMATH Keywords

performancerobustness analysissample sizerandomized algorithmsuncertain parametersprobabilistic approachunderperformance

Mathematics Subject Classification ID

Sensitivity (robustness) (93B35) Control/observation systems with incomplete information (93C41)

Related Items (12)

A probabilistic framework for problems with real structured uncertainty in systems and control ⋮ A survey of randomized algorithms for control synthesis and performance verification ⋮ A probabilistic point of view on peak effects in linear difference equations ⋮ Probabilistic robustness analysis: Explicit bounds for the minimum number of samples ⋮ A sampling-and-discarding approach to chance-constrained optimization: feasibility and Optimality ⋮ On the binomial confidence interval and probabilistic robust control ⋮ Research on probabilistic methods for control system design ⋮ Application of randomized algorithms to assessment and design of observer-based fault detection systems ⋮ Discussion on: ``Why is resorting to fate wise? A critical look at randomized algorithms in systems and control ⋮ A New Probabilistic Robust Control Approach for System with Uncertain Parameters ⋮ A probabilistic solution of robustH_∞control problem with scaled matrices ⋮ A new statistical approach for the analysis of uncertain systems

Cites Work

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• Several NP-hard problems arising in robust stability analysis
• The uniform distribution: A rigorous justification for its use in robustness analysis
• Probabilistic robustness analysis: Explicit bounds for the minimum number of samples
• A Monte Carlo approach to the analysis of control system robustness
• Checking robust nonsingularity is NP-hard
• Stochastic robustness of linear time-invariant control systems
• Computational complexity of μ calculation
• NP-Hardness of Some Linear Control Design Problems
• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

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