Robust stabilization of exponentially unstable linear systems with saturating actuators

For an exponentially unstable linear system subject to actuator saturation, a family of linear feedback laws is constructed that achieves semi-global practical stabilization on the null controllable region in the presence of bounded disturbance. This is in the sense that, for any (arbitrarily large) compact subset χ₀ of the null controllable region C, any (arbitrarily small) set χ₀ containing the origin in its interior, and any (arbitrarily large) bound on the disturbance, there is a feedback law from the family such that any trajectory of the closed-loop system enters and remains in the set χ₀, in a finite time as long as it starts from the set χ₀