We present a new actuator fault tolerant control strategy for linear, discrete-time systems. The scheme consists of three modules: a bank of estimators, each one associated with healthy and faulty model configurations, a logic mechanism for identifying healthy-to-faulty and faulty-to-healthy transitions, an estimate based control reconfiguration unit. The idea is to abstractly describe healthy and faulty plant configurations by means of a switching system and to make use sequences of pre-computed inner approximations of the one-step controllable sets associated to the obtained model configurations. Such sets are then on-line exploited together with a switching logic to determine the current plant configuration on the basis of the estimate state provided by the observers.