This paper presents a Fault Tolerant Control scheme for constrained discrete time linear systems against stuck actuators and bounded disturbances. The results here proposed are a significant generalization of a similar algorithm which has been designed only to manage healthy/out-of-service in the actuator units. A first key feature is the capability to exploit existing methods based on polyhedral algebra and computational geometry in order to characterize the reconfiguration logic of the proposed fault tolerant architecture. This is achieved by defining a set of a finite number of piecewise affine systems capable to cover all of the admissible faulty stuck scenario. It is then proved that one-step sequences of controllable sets can be formally defined within a piecewise affine system paradigm under the key property that each region is a polygon.