In this book, the focus is on two control problems for non-smooth systems. Firstly, the disturbance attenuation problem for piecewise linear (PWL) and piecewise affine (PWA) systems is studied. Here, we focus on applications in the field of perturbed flexible mechanical systems with PWL restoring characteristics. Secondly, the stabilization problem for Lur'e type systems with set-valued nonlinearities is examined. In the latter context, the focus is on the application area of mechanical systems with set-valued friction characteristics, where the friction is non-collocated with the control action. To deal with both the disturbance attenuation and the stabilization problem, observer- based output-feedback control strategies are proposed. To show the strengths, weaknesses and potential of output-feedback controllers beyond their theoretical importance, it is indispensable to evaluate them in experimental setups. Therefore, the presented strategies are implemented to two case studies: i) a PWL system, ii) a dynamic rotor system with friction. These case studies can be considered as benchmarks for the proposed strategies for non- smooth and discontinuous systems.