In this thesis, the stability and performance of closed-loop systems following the loss of sensors or feedback signals (sensor faults) are studied. The objective is to guarantee stability in the face of sensor faults while optimising performance under nominal (no sensor fault) condition. One of the main contributions of this work is to deal effectively with the combinatorial binary nature of the problem when the number of sensors is large. Several fault-tolerant controller and observer architectures that are suitable for different applications are proposed and their effectiveness demonstrated. The problems are formulated in terms of the existence of feasible solutions to linear matrix inequalities. The formulations presented in this work are described in a general form and can be applied to a large class of systems. In particular, the use of fault-tolerant architectures for damping inter-area oscillations in power systems using wide-area signals has been demonstrated. As an extension of the proposed formulations, regional pole placement to enhance the damping of inter-area modes has been incorporated. The objective is to achieve specified damping ratios for the inter-area modes and maximise the closed-loop performance under nominal condition while guaranteeing stability for all possible combinations of sensors faults. The performances of the proposed fault-tolerant architectures are validated through extensive nonlinear simulations using a simplified equivalent model of the Nordic power system.