In this paper, the outputs of a nonlinear system are divided into two groups: outputs of sensors which areprotected, and outputs of sensors which are prone to get attacked. A higher-order sliding-mode observer is used to estimate the states ofsystem and plantattacks. Equal to the number of outputs under protection, the input plant attacks can be reconstructed asymptotically, whilst the rest of the attacks can be identified byaSparse recovery method. Finally, simulation results froma real electric power system illustrateefficacy of theproposed observer