In the fault tolerant control (FTC) problem based on fault compensation a bi-directional uncertainty coupling exists between the controller and the joint state/fault estimation. This coupling arises from (a) the model mismatch between the system dynamics and the observer model as well as (b) the uncertainty arising from imperfect fault estimation. Hence, this paper deals with an approach to integrate together the designs of the observer and controller for a linear system subject to bounded actuator and sensor faults as well as disturbance. The fault estimation is achieved by using an augmented state form of an unknown input observer (UIO) which relaxes the well-known UIO rank restriction in terms the system coefficient matrices. The integrated design problem with fault compensation is an observer-based robust control system solved via H∞ optimization using single-step LMI formulation. The closed-loop system time response is improved using LMI regional pole placement. The FTC performance is illustrated using an example with both sensor and actuator faults as well as disturbance and uncertainty.