This paper proposes synthesis algorithms for the design of passive state- and output-feedback fault-tolerant controllers. Sufficient conditions for the existence and the construction of such fault-tolerant controllers are given in terms of linear matrix inequalities (LMIs) which can be solved efficiently. The state-feedback fault-tolerant controller consists of a family of state-feedback gains switched appropriately according to a stabilizing switching signal so that the closed-loop system satisfies a performance requirement expressed in terms of system norm. Similarly, the output feedback controller consists of a family of full-order linear, time-invariant controllers switched according to a stabilizing signal that depends only on the controller states. Both approaches are passive in the sense that they do not rely on the detection and/or the estimation of the faults. The proposed approaches are tested on a nonlinear model of a quadcopter. Simulation results show that satisfactory stability, tracking, and disturbance rejection are maintained despite of time-varying actuator faults.