Balancing control is important for biped standing. In spite of large efforts, it is very difficult to design balancing control strategies satisfying three requirements simultaneously: maintaining postural stability, improving energy efficiency, and satisfying the constraints between the biped feet and the ground. To implement such a control, inclusion of the actuators' dynamics is necessary, which complicates the overall system, obstructs the control design, and makes stability analysis more difficult. In this paper, a constrained balancing control meeting all three requirements is designed for a standing bipedal robot. The dynamics of the selected actuators has been considered for developing the motion equations of the overall control system, which has usually been neglected in simulations. In addition, stability analysis of such a complex biped control system has been provided using the concept of Lyapunov exponents (LEs), which shows the significance of actuators' dynamics on the stability region. The paper contributes to balancing standing biped in both the theoretical and the practical sense.