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

Constantino M. Lagoa, Fabrizio Dabbene, Roberto Tempo

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3178-3187
Number of pages10
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number10
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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