The concept of friction-induced brake vibrations, commonly known as judder, is investigated. Judder vibration is based on the class of geometrically induced or kinematic constraint instability. After presenting the modal coupling mechanism and the associated dynamic model, a stability analysis as well as a sensitivity analysis have been conducted in order to identify physical parameters for a brake design avoiding friction-induced judder instability. Next, in order to reduce the size of the instability regions in relation to possible system parameter combinations, robust stability via μ-synthesis is applied. By comparing the unstable regions between the initial and controlled brake system, some general indications emerge and it appears that robust stability via μ-synthesis has some effect on the instability of the brake system.