As one of dynamics-based control of biped walking, some researchers presented the control method to take advantage of robot dynamics directly by use of point-contact state between a robot and the ground. We proposed Passive Dynamic Autonomous Control (PDAC) previously[13] as one of point-contact methods. PDAC expresses the robot dynamics as an 1-dimensional autonomous system based on the two concepts: 1) point-contact 2) Virtual Constraint (proposed by Grizzle and Westervelt et al[8], [10]). We actually realized 3D dynamic walking by means of proposed method, however stability is not proved and the convergence domain is not clear. Thus, this paper finds the convergence domain of the previously proposed controller and proves the stability by the Liapunov Theory. Finally, the correctness of stability proof is confirmed by the numerical simulation.