This paper presents a fault-tolerant control scheme for constrained discrete-time linear systems against stuck actuators and bounded disturbances. The results proposed here are a significant generalization of a similar algorithm that has been designed only to manage healthy/out-of-service actuator units. A key feature of the proposed scheme consists of taking advantage of polyhedral algebra and computational geometry concepts in order to characterize the reconfiguration logic of the proposed fault-tolerant architecture. This is achieved by describing the plant via a set of a finite number of piecewise affine (PWA) systems capable to cover all the admissible faulty stuck scenarios. It is then proved that one-step sequences of controllable sets can be formally defined within a PWA system paradigm under the key property that each region is a polyhedron.