This paper deals with the attitude control problem of flexible satellite system under time varying disturbance, actuator fault and input time-delay. Initially, in order to compensate for the negative effects of the disturbance and fault, two observer designs are proposed to obtain their estimations, respectively. Secondly, by combining anti-disturbance control, fault tolerant control and time-delay control approaches, a composite delay-dependent controller is presented and an augmented closed-loop system is derived. Then, based on Lyapunov stability theory and linear matrix inequality (LMI) approach, two sufficient conditions on ensuring the asymptotical stability and H-infinity performance index are established, in which the observer gains and controller one can be computed by resorting to the Mat lab LMI Toolbox. Finally, some simulations and comparisons are provided to illustrate the effectiveness and advantages of the proposed control methods. (C) 2021 Elsevier Inc. All rights reserved.