Hard Bounds on the Probability of Performance With Application to Circuit Analysis

In this paper, we address the problem of analyzing the performance of an electrical circuit in the presence of uncertainty in the network components. In particular, we consider the case when the uncertainties are known to be bounded and have probabilistic nature, and aim at evaluating the probabilit...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2008-11, Vol.55 (10), p.3178-3187
Main Authors: Lagoa, C.M., Dabbene, F., Tempo, R.
Format: Article
Language:English
Subjects:
Asymptotic properties
Circuit analysis
Circuit simulation
Circuit stability
Circuits
control theory
Electric circuits
Iterative algorithms
ladder networks
Mathematical models
Monte Carlo methods
Networks
Numerical simulation
Performance analysis
probabilistic methods
randomized algorithms
resistive circuits
Robust control
Robustness
Studies
Uncertainty
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Summary:In this paper, we address the problem of analyzing the performance of an electrical circuit in the presence of uncertainty in the network components. In particular, we consider the case when the uncertainties are known to be bounded and have probabilistic nature, and aim at evaluating the probability that a given system property holds. In contrast with the standard Monte Carlo approach, which utilizes random samples of the uncertainty to estimate ldquosoftrdquo bounds on this probability, we present a methodology that provides ldquohardrdquo (deterministic) upper and lower bounds. To this aim, we develop an iterative algorithm, based on a property oracle , which is shown to converge asymptotically to the true probability of property satisfaction. Construction of the property oracles for specific applications in circuit analysis is explicitly presented. In particular, we study in full detail the problems of assessing the probability that the gain of a purely resistive network does not exceed a prescribed value, and of evaluating the probability of stability of an uncertain network under parameter variations. The paper is accompanied by illustrating examples and extensive numerical simulations.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2008.923436