Output feedback control for systems with constraints and saturations: Scalar control case

We consider the problem of regulating the state of a linear system within a prescribed region of the state-space in the presence of disturbances and control saturations. While prior work has focused on full state-feedback, we consider the case of noisy output feedback. For the scalar control case, we combine existing work on full state-feedback and set-valued observers to derive a computational procedure which determines a priori whether the desired constrained regulation is possible. Furthermore, we show that constrained regulation can always be achieved by a set-valued observer followed by static feedback.