Practical Stabilization on Null Controllable Region

Abstract

In the previous chapters, we have characterized the asymptotically null controllable region of a linear systems subject to actuator saturation. We have also constructed stabilizing feedback laws that would result in a domain of attraction that is either the entire asymptotically null controllable region or a large portion of it. In this chapter, we start to address closed-loop performances beyond large domains of attraction. In particular, we will design feedback laws that not only achieve semi-global stabilization on asymptotically null controllable region but also have the ability to reject input-additive bounded disturbances to an arbitrary level of accuracy. We refer to such a design problem as semi-global practical stabilization on the null controllable region