In this paper a nonlinear suboptimal stabilizing control strategy based on Control Lyapunov Functions (CLF) is synthesized and applied to a quadrotor helicopter. Sufficient conditions are obtained for this control law to ensure the asymptotic stability of the closed loop system. Furthermore, a particular methodology to find a CLF candidate for nonlinear affine system is also presented, which is highly relevant because the dynamical model representing the VTOL aerial vehicles have this affine structure. Using this CLF candidate, we are able to synthesize a nonlinear stabilizing optimal control law which allows energy saving. Numerical simulations were developed for both control strategies and real time experiments have been performed using the nonlinear stabilizing control algorithm. The numerical simulations have shown a successful performance of the autonomous aerial vehicle.