A µ-analysis based approach to probabilistic delay margin analysis of uncertain linear systems*
Résumé
Monte Carlo and deterministic µ-analysis are well known tools in aerospace industry for Validation and Verification (V&V) purposes. On the one hand, Monte Carlo analysis can provide an accurate measure of probability for sufficiently frequent phenomena. Nevertheless, it is often timeconsuming and may fail to compute worst-case stability margins and performance levels. Deterministic µ-analysis, on the other hand, cannot miss worst-case scenarios. But in the absence of a measure of probability, a control system may be invalidated on the basis of extremely rare events. About twenty years ago, probabilistic µ-analysis was therefore introduced to bridge the analysis gap between both techniques. It combines efficient µbased algorithms with a branch-and-bound scheme to explore the whole uncertainty domain, also considering probability distributions on the uncertain parameters. In this context, this paper describes a novel algorithm for probabilistic delay margin analysis, which provides upper and lower bounds on the probability of an uncertain system violating a desired delay margin.
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