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This paper proposes a second-order sliding mode observer for fault diagnosis (FD) of a class of uncertain dynamical systems. In the proposed FD scheme, a modified super-twisting second-order sliding mode algorithm is firstly established to observe the system state in the presence of uncertainties and disturbances, and then the observer input is designed by using a PID-type iterative learning algorithm to detect, isolate, and estimate faults. The convergence of the sliding mode algorithm and the parameter update law for the iterative learning estimator are both theoretically and rigorously studied. Finally, the proposed fault diagnosis scheme is applied to the dynamics of a satellite with flexible appendages, and the simulation results demonstrate its effectiveness.