The primary goal of this paper is to develop an analytical framework to systematically design dynamic output feedback controllers that exponentially stabilize multi-domain periodic orbits for hybrid dynamical models of robotic locomotion. We present a class of parameterized dynamic output feedback controllers such that (1) a multi-domain periodic orbit is induced for the closed-loop system, and (2) the orbit is invariant under the change of the controller parameters. The properties of the Poincare map are investigated to show that the Jacobian linearization of the Poincare map around the fixed point takes a triangular form. This demonstrates the nonlinear separation principle for hybrid periodic orbits. We then employ an iterative algorithm based on a sequence of optimization problems involving bilinear matrix inequalities to tune the controller parameters. A set of sufficient conditions for the convergence of the algorithm to stabilizing parameters is presented. Full state stability and stability modulo yaw under dynamic output feedback control are addressed. The power of the analytical approach is ultimately demonstrated through designing a nonlinear dynamic output feedback controller for walking of a 3D humanoid robot with 18 state variables and 325 controller parameters.