Output Regulation — Discrete-Time Systems

In Chapter 12, we systematically studied the problem of output regulation for continuous-time linear systems subject to actuator saturation. In particular, we characterized the regulatable region, the set of plant and exosystem initial conditions for which output regulation is possible with the saturating actuators. It turned out that the asymptotically regulatable region can be characterized in terms of the null controllable region of the anti-stable subsystem of the plant. We then constructed feedback laws that achieve regulation on the regulatable region. These feedback laws were constructed from the stabilizing feedback laws in such a way that a stabilizing feedback law that achieves a larger domain of attraction leads to a feedback law that achieves output regulation on a larger subset of the regulatable region and, a stabilizing feedback law on the entire asymptotically null controllable region leads to a feedback law that achieves output regulation on the entire asymptotically regulatable region