Control of crosswind kites is very important subject in the pumping kite system, which is one of expected ways of wind power generation. Although many ways to control them are proposed before, any commercial operations haven't been succeeded for some reasons. In this study, stability verified controller for the pumping kite system is designed. In order not to make the controller too complicated, the kite model is simplified to be independent to some variables. Controller for the traction phase of the pumping kite system is designed based on the method proposed in the field of robotics. In that method, trajectories generation by optimal control, designing time varying LQR, and stability verification are repeated. About the controller for the retraction phase, standard LQR is designed and stability is verified using SOS programming. Designed two controllers are switched by length of the tether of the kite. Then, simulation is conducted with more practical kite model than control model.