We formulate a new criterion over a frequency region for a fault-tolerant control problem with disturbances as a mathematical problem. We present all solutions to this problem for linear time-invariant descriptor systems and apply them to find a passive fault-tolerant controller with a sufficient level of disturbance attenuation for two classes of systems: the first one includes systems in which a rational matrix has a constant inertia in the frequency region, and the second class includes systems in which the number of controls is not greater than the number of controlled outputs. Three examples are given to illustrate the feasibility of our two-step control design algorithm.