Probabilistic robustness: an RLC circuit realization of the truncation phenomenon

A previously developed paradigm for probabilistic robustness analysis does not require a priori information about the underlying distribution function for the uncertain parameters; only a mild monotonicity and symmetry assumption is involved. The starting point is exactly the same as in classical robustness theory-a system with uncertain parameters which are only known within given bounds. However, instead of calculating the classical robustness margin for such a system, a risk-adjusted margin is sought. The theory suggests that the "best" way to sample the uncertain parameters is not necessarily the most intuitive way. That is, the sampling distribution to use is not something obvious such as a normal or uniform distribution. The main objective of this paper is to demonstrate that these "counterintuitive" predictions of the theory are not just mathematical possibilities but actually admit physical realizations. To this end we consider a two stage RLC amplifier with random parameters corresponding to independent uncertainties in the capacitors.