In this paper, the simultaneous stabilisation problem is addressed for a collection of time-delay nonlinear systems which are perturbed by time-varying norm-bounded uncertainties. The time-delay is considered to change within an interval. A design procedure for constructing a simultaneously stabilising sliding mode output feedback controller is presented. At first, by applying a delay-range-dependent stability analysis, sufficient conditions concerned with the existence of a common sliding surface are derived which are then transformed into the LMI-based conditions. Finally, a robust simultaneously stabilising control law is proposed to drive all the systems to the sliding surface in finite-time. A numerical example is included to demonstrate the effectiveness of the proposed method.