An H-infinity-based Lyapunov proof is provided for a result recently established by Lin and Saberi : if a linear system is asymptotically null controllable with bounded controls then, when subject to input saturation, it is semi-globally stabilizable by linear state feedback. A new result is that if the system is also detectable then it is semi-global stabilizable by completely linear output feedback. Further, an extension which relaxes the requirements on the input characteristic is obtained.