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In this paper, the robust exponential <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> fault tolerant control problem is investigated, which is concerned with uncertainties, disturbances and actuator failures. Determined by whether the actuator fails or not, the continuous-time system is remodeled as a switched system. Then a sampled-data controller is designed. Through Lyapunov functional theory and the admissible edge-dependent average dwell time method, some sufficient conditions are derived to ensure that the closed-loop system is robustly exponentially stable with exponential <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance. The corresponding controller gains can also be obtained via linear matrix inequalities (LMIs). Finally, two examples are presented to verify the validity of the relevant results.