A persistent concern of control engineering is the performance of systems in the presence of uncer-tainty. In this paper, we consider uncertainties affecting systems as stochastic processes of independentstationary increments. We show that in many situations the performance of an uncertain system canbe measured by a function of a parametric stopping time and associated values of stochastic processes.Under some mild regularity conditions, we demonstrate that the performance measure is governed bystochastic functional central limit theorems as the parameters of the stopping time tend to certain val-ues. Such results can be applied to the analysis and design of control systems affected by uncertainties.
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