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This paper deals with the characterization of reachable domain of a set-point controller for a cable-suspended robot under disturbances and input constraints. The main contribution of the paper is to calculate the feasible domain analytically through the choice of a control law, starting from a given initial condition. This analytical computation is then recursively used to find a second feasible domain starting from a boundary point of the first feasible domain. Hence, this procedure allows to expand the region of feasible reference signals by connecting adjacent domains through common points. Finally, the effectiveness of the proposed method is illustrated by numerical simulations on a kinematically determined cable robot with six cables.