The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported in the literature. The primary characteristic of this modified control law is that more design parameters,which are the closed-loop eigenvalues when the system is operating in linear form,are introduced and which can be well designed to achieve better system performance. Using this law,the pole locations of the closed-loop systems depending on a linear transformation can be placed arbitrarily within certain areas. Numerical example shows that the performance of the closed-loop system under this control law can be significantly improved if the free parameters are properly chosen. The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported in the literature. The primary characteristic of this modified control law is that more design parameters, which are the closed-loop eigenvalues ​​when the system is operating in linear form, are introduced and which can be well designed to achieve better system performance. Using this law, the pole locations of the closed-loop systems depending on a linear transformation can be placed arbitrarily within certain areas. Numerical example shows that the performance of the closed-loop system under this control law can be significantly improved if the free parameters are properly chosen.