The paper solves the problem of simultaneous stabilization of continuous-time linear systems subject to input saturation, where both global asymptotic stability, in the absence of external input disturbance, and global \(L_{p}\) stability with finite gain of the closed loop system are required. In particular, it is shown that for any \(p\), the simultaneous stabilization problem is solvable, provided that the pair \((A,B)\) of the given system is stabilizable and the eigenvalues of \(A\) are in the closed left half complex plane. Notice that the above two assumptions can be made without loss of generality, since it is well known that they are necessary to solve the problem via state feedback. A new stabilizing family of scheduled low-and-high gain state feedback laws is given. Moreover, such a family is equipped with a design parameter that can be adjusted to make the disturbance to output \(L_{p}\) gain of the closed-loop system arbitrarily small.