Unmanned ground vehicles (UGV) may experience skidding when moving at high speeds, and therefore have its safety jeopardized. For this reason the nonlinear dynamics of lateral tire forces must be taken into account into the design of steering controllers for autonomous vehicles. This paper presents the design of a state feedback piecewise affine controller applied to an UGV to coordinate the steering and torque distribution inputs in order to reduce vehicle skidding on demanding maneuvers. The control synthesis consists in solving an optimization procedure involving constraints in the form of Linear Matrix Inequalities which are obtained from stability conditions of a piecewise quadratic Lyapunov function. The improved performance of the piecewise affine controller with respect to a linear controller is confirmed through simulations on degraded tire-floor adhesion.