The goal of this paper is to approximate the worst-case transient performance of uncertain linear time-invariant systems, subject to both L2-bounded input signals and known disturbances, e.g., reference tracking commands. System uncertainties are described through real-valued random variables with a known probability distribution. The worst-case performance analysis is formulated as a parametric Riccati differential equation, which is approximately solved using polynomial chaos expansion. The objective is to estimate a bound on the Euclidean norm of the system output at a given time. The effectiveness of the approach is demonstrated on the example of a spacecraft attitude and orbit control system.