This paper investigates actuator fault detection and isolation for discrete-time linear descriptor systems. We propose a novel fault detection and isolation scheme based on a bank ofH-/L infinity fault detection observers (FDOs). Under the assumption that the disturbances are unknown but bounded,L infinity analysis is used to attenuate the effects of disturbances. Meanwhile, the FDO is designed to be sensitive to the fault via considering theH-performance index in finite frequency domain. The design conditions of the proposed FDO are converted into solving a set of linear matrix inequalities. Furthermore, the residual evaluation based on a set-membership approach is proposed to reduce conservatism. Simulation results are provided to demonstrate the performance of the proposed method.