This work is motivated through a research study ADDSAFE funded by the European Commission, following an interest in implementing mixed linear parameter varying (LPV) H_/H✓ model-based fault detection and diagnosis (FDD) methodology for detecting nonlinear actuator faults for flight control system. The main design goal is to maximize the robustness of the residual signal to uncertainty and disturbances whilst also achieving the specific minimum sensitivity of the residual signal to faults. The specific minimum sensitivity index used is based on the H_ index concept and is extended to the LPV FDD system problem. This allows the fault signature for multiple sensor and actuator faults to be reconstructed simultaneously, facilitating the robust isolation of faults rather than just their detection. Instead of using constant gains, parameter-varying gains are used in the LPV observer and the free design parameters generated, through using the generalized inverse, can be parameterized to improve the conservatism of finding the robust solution. This approach is combined within the standard quadratic LPV framework. The FDD approach developed is then applied in non-linear simulation to the example of faults in the left elevator and aileron of a large transport aircraft.