Output regulation of linear systems with bounded continuous feedback

Abstract—This paper studies the classical problem of output regulation for linear systems subject to control constraint. The asymptotically regulatable region, the set of all initial conditions of the plant and the exosystem for which output regulation is possible, is characterized in terms of the null controllable region of the antistable subsystem of the plant. Continuous output regula-tion laws, of both state feedback type and error feedback type, are constructed from a given stabilizing state feedback law. It is shown 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 asymptotically regulatable region. A feedback law that achieves global stabilization on the asymptoti-cally null controllable region leads to a feedback law that achieves output regulation on the entire asymptotically regulatable region. Index Terms—Bounded control, nonlinear control, output regu-lation, regulatable region. I