The novel contribution of the thesis is the design and implementation of decentralised output feedback power system controllers for power oscillation damping (POD) over the entire operating regime of the power system. The POD controllers are designed for the linearised models of the nonlinear power system dynamics. The linearised models are combined and treated as parameter varying switched systems. The thesis contains novel results for the controller design, bumpless switching and stability analysis of such switched systems. Use of switched controllers against the present trend of having single controller helps to reduce the conservatism and to increase the uncertainty handling capability of the power system controller design. Minimax-LQG control design method is used for the controller design. Minimax-LQG control combines the advantages of both LQG and H control methods with respect to robustness and the inclusion of uncertainty and noise in the controller design. Also, minimax-LQG control allows the use of multiple integral quadratic constraints to bound the different types of uncertainties in the power system application. During switching between controllers, switching stability of the system is guaranteed by constraining the minimum time between two consecutive switchings. An expression is developed to compute the minimum time required between switchings including the effect of jumps in the states. Bumpless switching scheme is used to minimise the switching transients which occur when the controllers are switched. Another contribution of the thesis is to include the effect of on load tap changing transformers in the power system controller design. A simplified power system model linking generator and tap changing transformer dynamics is developed for this purpose and included in the controller design. The performance of the proposed linear controllers are validated by nonlinear computer simulations and through real time digital simulations. The designed controllers improve power system damping and provide uniform performance over the entire operating regime of the generator.