TY - JOUR

T1 - Hard bounds on the probability of performance with application to circuit analysis

AU - Lagoa, Constantino M.

AU - Dabbene, Fabrizio

AU - Tempo, Roberto

PY - 2008

Y1 - 2008

N2 - 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 "soft" bounds on this probability, we present a methodology that provides "hard" (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.

AB - 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 "soft" bounds on this probability, we present a methodology that provides "hard" (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.

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U2 - 10.1109/TCSI.2008.923436

DO - 10.1109/TCSI.2008.923436

M3 - Article

AN - SCOPUS:57149143856

VL - 55

SP - 3178

EP - 3187

JO - IEEE Transactions on Circuits and Systems I: Regular Papers

JF - IEEE Transactions on Circuits and Systems I: Regular Papers

SN - 1549-8328

IS - 10

ER -