The robust fault-tolerant control design problem of second-order linear systems via eigenstructure assignment
is investigated. The aim is to redesign a state feedback control law such that the fault closed-loop system has the same eigenvalues with the normal close-loop system, the eigenvectors of the fault closed-loop system are as close to those of the normal close-loop system as possible in terms of least squares, and the sensitivity is minimized to improve the system robustness. Based on the parameterized result of state feedback eigenstructure assignment, the optimal problem of sensitivity is changed into an optimal problem with some constraint conditions, and the robust fault-tolerant control design method is proposed. Finally, a numerical example and its simulation results show the effectiveness of the proposed design method.