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This paper studies the fault-tolerant control (FTC) problem of actuator failure compensation in continuous-time systems using linear matrix inequality (LMI) approach and adaptive design method, respectively. The LMIs are developed with parameter-dependent Lyapunov function to find a stabilizing state-feedback controller such that the nominal H infin performance is optimized for the actuator failure cases, which can also reduces the conservatism of the design. The adaptation laws are proposed to estimate unknown eventual faults on actuators on-line. Then a class of state feedback controllers are constructed for automatically compensating the fault effects based on the information from adaptive scheme for guaranteeing the stability via Lyapunov stability theory. The proposed design technique is finally evaluated in the light of simulation examples.