Null Controllability and Stabilization of Linear Systems Subject to Asymmetric Actuator Saturation

In regard to stabilizability, it is shown in [12] that a linear system subject to actuator saturation can be globally asymptotically stabilized by smooth feedback if and only if the system is asymptotically null controllable with bounded controls (ANCBC), which, as shown in [10,11], is equivalent to the system being stabilizable in the usual linear sense and having open loop

poles in the closed left-half plane. A nested feedback design technique for designing nonlinear globally asymptotically stabilizing feedback laws was proposed in [14] for a chain of integrators and was fully generalized in [13].