This paper introduces a problem of robust control with a terminal state constraint. This problem involves finding an output feedback controller to steer the initial state of a given system into an ellipsoidal bounding set in a specified time. The underlying system in this problem is a time-varying uncertain linear system in which the uncertainty satisfies an integral quadratic constraint. Necessary and sufficient conditions are given for the solution to this problem in terms of a pair of parameter-dependent Riccati differential equations.