We present a method to parameterize a Lyapunov function for nonlinear switched systems using linear programming. The method always works if the system at hand has an asymptotically stable equilibrium. Further, we discuss how this method can be adapted to computing control Lyapunov functions and controllers. However, in this case the resulting optimization problem is a mixed-integer linear feasibility problem, which implies that the computational cost increases rapidly with the complexity of the controller.