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A set invariance condition for a piecewise continuous time-varying system is developed and applied to the fault-tolerant control problem against the actuator effectiveness loss for linear systems subject to system uncertainties and actuator saturation in this study. Linear matrix inequality conditions are proposed to compute invariant ellipsoidal sets. Discussions on system performance optimisation are given including reduction on computational complexity, maximisation of the domain of attraction and disturbance rejection. The proposed design techniques are applied to an unstable multi-input and multi-output system and to the flight control of a non-linear unmanned aerial vehicle model subject to the control effectiveness loss fault in the elevator.