Smooth state feedback stabilization for a family of planar switched nonlinear systems is addressed. Based on the approach called adding a power integrator, the task of finding a common Lyapunov function and that of designing state stabilizing feedback laws for the switched nonlinear system whose subsystems may have uncontrollable/unobservable Jacobian linearization are solved simultaneously. Globally asymptotical stabilization of the switched nonlinear system under arbitrary switchings is achieved by the state feedback control. Numerical examples are employed to verify the efficiency of the proposed method.