A novel workspace, called Control Stability Workspace~(CSW), is proposed and analyzed in this paper. It is a workspace from the control perspective. It allows us to determine whether the closed-loop controller will be able to guide a cable-driven parallel robot~(CDPR) to a desired pose, given that there are perturbations present in the system. The effect of the different perturbations on the CSW is analyzed for two spatial CDPRs with a pose-based visual servoing~(PBVS) controller. Indeed, this workspace is not only robot architecture-dependent, but also control-dependent. It was found that the model errors, that is, the errors in the cable exit and anchor point coordinates, have the most significant effect on the CSW. However, if the pulleys are small enough, then neglecting their geometry does not lead to a significant reduction of the workspace.