This paper addresses the stabilization of a class of nonlinear systems in the presence of disturbances, using hybrid control. To this effect we introduce two new classes of switched systems and provide conditions under which they are input-to-state practically stable (ISpS). These results lead to a control design methodology called switched seesaw control design that allows for the development of nonlinear control laws yielding input-to-state stability, using switching. The range of applicability and the efficacy of the methodology proposed are illustrated via two non-trivial design examples. Namely, stabilization of the extended nonholonomic double integrator (ENDI) and stabilization of an underactuated autonomous underwater vehicle (AUV) in the presence of input disturbances and measurement noise.