The development of any fault-tolerant control solution is based on the strong assumption that fault situations can be accommodated. This paper provides a survey of four reachable set techniques to assess the fault recoverability property for constrained linear time invariant (LTI) systems by means of ellipsoid, zonotope, polytope and support function representations. These techniques are next applied to an angular velocity spacecraft model. A discussion is finally made to assess the computational complexity for the four algorithms
