In this note, a novel actuator Fault Tolerant Control strategy for constrained discrete time linear systems subject to bounded disturbances is proposed. 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 and an estimate based control reconfiguration unit. The idea is to abstractly describe healthy and faulty plant configurations by means of a switching paradigm and sequences of pre-computed inner approximations of one-step controllable sets. Such regions are then on-line exploited together with a switching logic to determine the current plant configuration on the basis of the state estimate provided by the observers.