We propose a weighted subtask controller and sufficient conditions for boundedness of the controller both velocity and acceleration domain. Prior to designing the subtask controller, a task controller is designed for global asymptotic stability of task space error and subtask error. Although the subtask error converges to zero by the task controller, the boundedness of the subtask controller is also important, therefore its boundedness conditions are presented. The weighted pseudo inverse is introduced to relax the constraints of the null-space of Jacobian. Using the pseudo inverse, we design subtask controller and propose sufficient conditions for boundedness of the auxiliary signal to show the existence of the inverse kinematic solution. The results of experiments using 7-DOF WAM show the effectiveness of the proposed controller.