A wheel slip controller for Anti-lock Brake Systems (ABS) is designed using LQ-optimal control. The controller gain matrices are gain scheduled on the vehicle speed. A parameter dependent Lyapunov function for the nominal linear parameter varying (LPV) closed loop system is found by solving a linear matrix inequality (LMI) problem. This Lyapunov function is used to investigate robustness with respect to uncertainty in the road/tyre friction characteristic. Experimental results from a test vehicle with electromechanical brake actuators and brake-by-wire show that high performance and robustness are achieved.