The thesis considers the development of robust output feedback sliding mode controllers for linear time invariant uncertain systems where output information alone is available to the controller. Two approaches to controller design are discussed. The first uses only the plant dynamics and is called static output feedback sliding mode control. It is shown that a quadratically stable sliding motion may be attained for a bounded uncertain system if and only if the system is minimum phase and a particular subsystem triple satisfies the output feedback design criteria. Sliding mode controllers are sensitive to unmatched uncertainty. Hence a robust design is considered which minimises the effect of uncertainty. The second approach is developed for systems which have design difficulties when only the plant dynamics are considered. Extra dynamics are added and the method is called dynamic output feedback sliding mode control. Closed-loop analysis is carried out and stability of the augmented system is observed. Both controllers guarantee a stable sliding motion despite the presence of bounded uncertainty. Finally, two practical uncertain multivariate industrial examples demonstrate the theoretical developments. The first application is a helicopter model. The open loop dynamics have unstable poles with two stable invariant zeros, variations in model parameters and exhibit high levels of cross coupling. A model following sliding mode controller is used to force the plant outputs to track the outputs of an ideal model. Nonlinear simulation results show the practicality of the method. The second application considers the dynamic output feedback sliding mode control of an aircraft model. The system possesses unstable invariant zeros and requires a dynamic output feedback technique. Simulation results are obtained at different operating points to show the effect of unstable invariant zeros. The examples illustrate the benefits of these robust output feedback based sliding mode control developments.