This paper proposes a decoupling approach to the integrated design of fault estimation (FE) and fault tolerant control (FTC) for linear systems in the presence of unknown bounded actuator faults and perturbations. An adaptive sliding mode augmented state unknown input observer is developed to estimate the system state, actuator faults and perturbations, based on a descriptor augmentation strategy and the equivalent output injection concept. Subsequently, an adaptive backstepping FTC controller is designed to compensate the effects of the faults and perturbations acting on the system to ensure robust output tracking. In the proposed observer the effects of the control system perturbations are estimated and the fault effects are compensated to ensure that the FE function is decoupled from the FTC system. This leads to satisfaction of the Separation Principle under the framework of integrated design. When compared with the existing Ho optimization single-step integrated FE/FTC design approach, in this paper the FE/FTC decoupling and the perturbation compensation (in the control) together contribute to a new integrated FTC strategy with more design freedom, less complexity and higher robustness. Moreover, the proposed method is shown to be applicable to a wide class of faults, which can be differentiable or non-differentiable, and matched or unmatched. Comparative simulations of the tracking control of a DC motor are provided to demonstrate the performance effectiveness of the proposed approach. (C) 2017 Elsevier Ltd. All rights reserved.