On the Lp (ℓp) stabilization of open-loop neutrally stable linear plants with input subject to amplitude saturation

It 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¿[1,8). 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¿[1,8) 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.