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.
|Number of pages||20|
|Journal||International Journal of Robust and Nonlinear Control|
|Publication status||Published - 2003|
Shi, G., Saberi, A., & Stoorvogel, A. A. (2003). On the Lp (ℓp) stabilization of open-loop neutrally stable linear plants with input subject to amplitude saturation. International Journal of Robust and Nonlinear Control, 13(8), 735-754. https://doi.org/10.1002/rnc.743