AbstractIt has been shown that for asymptotically null controllable linear systems with input saturation and non‐input‐additive disturbances, there exist nonlinear control laws that achieve global stabilization and Lp (ℓp) stabilization without finite‐gain for any p∈[1,∞). Recently, it also has been shown that for a simple double integrator there is no saturated linear controller that can achieve Lp stabilization for p>2. In this paper, we show that if a linear system is open‐loop neutrally stable and stabilizable then there exist saturated linear control laws that achieve Lp (ℓp) stability for any p∈[1,∞) and for arbitrary initial conditions. As a byproduct, we also show that the closed‐loop system with a saturated linear control law has a nice property similar to linear systems, i.e., any vanishing disturbance produces a vanishing state with arbitrary initial condition. Copyright © 2003 John Wiley & Sons, Ltd.