This article presents the design of a lane departure avoidance system which is conceived to operate even in demanding manoeuvres with respect to the lateral vehicle dynamics. Piecewise affine state feedback and output feedback controllers are used to handle the nonlinear behaviour of the lateral tyre forces. The controllers are designed based on the search of a piecewise quadratic Lyapunov function casted as a bilinear matrix inequalities problem. Experimental tests demonstrate the performance of the controller in degraded road conditions.