In this paper, a new non-quadratic stabilization approach is used to stabilize a two-link robot manipulator. We use a non-quadratic Lyapunov function as a fuzzy blending of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The proposed approach is based on two assumptions. The first one assumes a proportionaty between multiple Lyapunov functions and the second one assumes upper bounds for the time derivative of the premise membership functions. Furthermore a fuzzy model reference tracking control scheme is proposed based on the T-S fuzzy model where external disturbances are taken into account. To illustrate the effectiveness of our proposal, the two-link robot model is used for different simulations.