In the context of antilock braking systems (ABS), we present a two-phase hybrid control algorithm based on the tyre extended braking stiffness (XBS), that is, on the slope of the tyre-road friction coefficient with respect to the wheel slip. Because the XBS cannot be directly measured, a switched observer is used to estimate it. With the proposed hybrid algorithm, the closed-loop trajectories of the system satisfy the conditions required for the observer to correctly estimate the XBS. Moreover, the braking distances are shorter than those obtained using a hybrid algorithm based on wheel deceleration thresholds.