This thesis addresses three problems related to the antilock braking system (ABS) in the context of the wheel dynamics: the estimation of the tyre extended braking stiffness (XBS) during an emergency braking situation, the control of the ABS based on the estimation of the XBS, and the estimation of the angular velocity and acceleration of the wheel from the measurements of an incremental encoder with imperfections. The general objective of this work is to develop tools aimed at improving the performance of braking systems by using techniques adapted from nonlinear control theory. The first part of the manuscript is devoted to the construction of a switched adaptive observer for the XBS, that is, an adaptive observer whose estimation gains switch between two possible values based on the sign of the system’s measured output. The stability of the observer is analyzed using tools for switched and cascaded systems, as well as concepts such as persistency of excitation and singular time-scale transformations. The second part of the manuscript is dedicated to the design of a control algorithm for the ABS. The control objective is formulated in terms of the XBS and a hybrid controller is designed so that the trajectories of the system satisfy the conditions required for the estimation of the XBS. The stability of the controller is analyzed using the Poincaré map. The third part of the manuscript focuses on the construction of an algorithm to estimate angular velocity and acceleration of the wheel and remove perturbations which are introduced by the encoder imperfections and whose amplitude and frequency are a function of the wheel's (real) position, velocity, and acceleration. The algorithm is based on the method known as time-stamping algorithm, as well as filtering and parameter estimation techniques. Experimental tests and numerical simulations illustrate the performance of the estimation and control algorithms presented in this thesis. In all cases our results are compared with respect to the state of the art.