This paper considers actuator fault detection and isolation (FDI) problem for a class of linear discrete-time systems with constant time-delay. Based on delay-free representation, a novel fault detection and isolation scheme based on a bank of L∞ fault detection observers (FDOs) is proposed. Under the assumption that the disturbances and measurement noise are unknown but bounded, L∞ performance is introduced to reduce the effects of disturbances. Meanwhile, the FDOs are designed to be sensitive to the fault by means of fault detectability indices and matrix. The design conditions of the proposed FDOs are derived in terms of Linear Matrix Inequalities (LMIs). Furthermore, a zonotopic analysis method is presented to achieve the residual evaluation. Simulation results are provided to demonstrate the performance of the proposed approach.