In this article, a robust adaptive fault-tolerant compensation control problem via sliding mode method is studied for linear systems with actuator faults, disturbances, and parameter uncertainties. Based on a matrix full-rank factorization technique of an input matrix, a new lemma is presented and proved. In terms of this lemma and the information from adaptive mechanism, actuator faults, especially outage of certain actuators, can be compensated for under an actuator redundancy assumption. Without requiring any fault detection and isolation mechanism, a sliding mode fault-tolerant controller is then designed to guarantee the asymptotic stability and disturbance attenuation, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults. Finally, a rocket fairing structural-acoustic model is used to demonstrate the effectiveness of the proposed design method.
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