Aircraft anti-skid systems are key to maintaining directional control during ground handling and must balance performance and robustness over a wide operational envelope. In particular, the impact of longitudinal speed on the braking dynamics induces an important coupling between the longitudinal and vertical dynamics due to the aerodynamic effects. In this paper, longitudinal slip-based and wheel speed deceleration-based anti-skid controllers are designed based on control-oriented models of the braking dynamics for an aircraft with a tricycle landing gear configuration. A gain-scheduling strategy is devised to achieve high performance and maintain stability during landing maneuvers. The stability of the resulting closed-loop system affected by parametric variability and discretization effects is later verified in the framework of Linear Parameter-Varying systems by formulating a set of efficient Linear Matrix Inequalities. The resulting anti-skid designs are successfully evaluated in a validated multibody simulator for a target aircraft.