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Systems biologists are often faced with competing models for a given experimental system. Performing experiments can be time-consuming and expensive. Therefore, a method for designing experiments that, with high probability, discriminate between competing models is desired. In particular, biologists often employ models comprised of polynomial ordinary differential equations that arise from biochemical networks. Unfortunately, the model discrimination problem for such systems is computationally intractable. Here, we examine the linear discrimination problem: given two systems of linear differential equations with the same input and output spaces, and uncertain parameters, determine an input that is guaranteed to produce different outputs. In this context, we show that (1) if linearizations of the two nonlinear models can be discriminated, then so can the original nonlinear model; and (2) we show a class of systems for which the linear discrimination problem is convex. The approach is illustrated on a biochemical network with an unknown structure.