We defined here control strategies to stabilize the equilibrium vertical posture of a two-link, a three-link and a five-link biped, explicitly taking into account the limits imposed on the amplitudes of the control torques. For each biped we use the Jordan form of its linear model to extract the unstable modes that we want to suppress with the feedback control. For the two-link biped, the control law is optimal. This means that the basin of attraction for its linear system is as large as possible, i.e., it coincides with the controllability domain. For the five-link biped several choices of torques are allowable because we have four torques and three unstable modes. Therefore, we define a criteria to compute these torques. All the numerical results in this paper are realistic. A perspective for the case of the three-link biped is to define a control law, for which the basin of attraction is as large as allowable.