The thesis describes the design of a novel non-linear controller for the plasma vertical position in a Tokamak that maximizes the stability region and is robust to certain disturbances and measurement noise. The plasma vertical position in a Tokamak can be open loop unstable with time-varying dynamics. The limitation in the output power of the control amplifier makes the time varying unstable system particularly difficult to control. Fixed-coefficient linear controllers usually fail to maintain control in the presence of large disturbances, like Edge Localized Modes (ELMs), which saturate the amplifier output. During the saturation period the vertical position of the plasma will grow exponentially with the unstable eigenvalue and may reach values that cannot be controlled by the energy provided by the control amplifier which is limited by economic restraints. The primary sources of disturbances and measurement noise that effect the vertical position are the ELMs and the 600Hz noise from the thyristor power supplies. The former are present during high energy confinement plasma configurations in the form pulses. A simple model structure is derived for the vertical position which includes the effect of the disturbances and the measurement noise and the control amplifier. The model is validated against experimental data from the JET and the COMPASS-D Tokamaks. A method to measure the maximum obtainable stability region of unstable systems subject to control limitations is derived and used to determine the conditions for a maximum stabilizer controller. A novel technique to determine the existence, the stability and the period of possible limit cycles for relay controlled systems is derived and used to determine the stability region of unstable systems incorporating relay controllers with and without time delays. A novel non-linear controller for the vertical position based on a discrete time adaptive near-minimum time algorithm (DANTOC) is designed to stabilize the system, to maximize the stability region and to be robust to the aforementioned sources of disturbances and measurement noise. The controller is tested in simulation for the JET Tokamak and the results demonstrate its feasibility in controlling the vertical position for different plasma configurations. The controller is also tested on the COMPASS-D Tokamak and the results demonstrate the improvement with respect to a simple linear P + D controller in the presence of the aforementioned sources of disturbances and measurement noise. The proposed controller represents a much better solution than existing conventional controllers for the control of the plasma vertical position for the new generation of Tokamaks.