This study uses a novel approach, integrating fault estimation and fault decoupling methods, in designing a new Takagi–Sugeno multiple integral unknown input observer (TSMIUIO)-based fault tolerant control (FTC) system. The motivation is to tackle the challenges underlined in designing observer-based FTC for non-linear systems affected by simultaneous time-varying actuator and sensor faults, exogenous input, and sensor noise. In such systems, the FTC design challenges are the constraints imposed by the structure of input/output matrices, the need of extending the order of the observer to estimate simultaneous faults, the bi-directional interaction caused by the state and faults’ estimation errors, and the unpredictable time behaviour of fault signals. These challenges motivate the proposal of TSMIUIO to (i) ensure acceptable FTC performance, irrespective of the time behaviour of sensor fault; (ii) relax the complexity of TSMIUIO by avoiding the use of extended state approach for estimating simultaneous faults; and (iii) eliminate the BDI in the estimated signals that feed the controller. The effectiveness of the proposed method is illustrated using a single-link flexible joint robot and translational oscillator with an eccentric rotational proof mass actuator benchmark.