We consider the example of a three-link planar biped walker with two passive links. The main objective is to design symmetric periodic gaits in flat ground, that can be exponentially stabilized by feedback control. To this end, we apply recent advances in nonlinear control, to propose a systematic procedure to the problems of gait synthesis and control design. The core of the method lays on a nontrivial coordinate transformation, in order to approach the problem in a state-dependent form. For gait synthesis, such procedure allows a reduction of the search space, with the feasibility of considering energetic performance for optimization. For control design, this allows to apply concepts of transverse linearization, to design a nonlinear feedback control law, which performance is studied by numerical simulations.