To maximize wind power extraction, a variable-speed wind turbine (VSWT) should operate as close as possible to its optimal power coefficient. The generator torque is used as a control input to improve wind energy capture by forcing the wind turbine (WT) to stay close to the maximum energy point. In general, current control techniques do not take into account the dynamical and stochastic aspect of both turbine and wind, leading to significant power losses. In addition, they are not robust with respect to disturbances. In order to address these weaknesses, a nonlinear approach, without wind speed measurement for VSWT control, is proposed. Nonlinear static and dynamic state feedback controllers with wind speed estimator are then derived. The controllers were tested with a WT simple mathematical model and are validated with an aeroelastic wind turbine simulator in the presence of disturbances and measurement noise. The results have shown better performance in comparison with existing controllers.