A system with nonholonomic constraints attracts its attention from the viewpoint of control theory because any conventional control cannot be applied directly to such a system. Since it cannot be stabilized by a static continuous feedback with constant gains, there are several control methods up to now by using a chained form etc. Among them, a switching control method using invariant manifold, which is considered as a generalized form for sliding mode control known as one of conventional switching control methods, and a quasi-continuous exponential stabilizing control method are proposed in a power form system with two inputs and three states or two inputs and n-states. In this study, as a new mehod, a switching control method using an invariant manifold as mentioned above is examined for a "double integrator system," known as an alternative canonical model for nonholonomic systems. In particular, stabilizing controllers are derived for the case of a kinematic model with two inputs and three states and for the case of a dynamic model with two inputs and five states, which is just as an "extended double integrator system." The effectiveness of the proposed controllers is demonstrated through simulations for a mobile robot with two independent driving wheels.