Properties of recoverable region and semi-global stabilization in recoverable region for linear systems subject to constraints

This paper investigates time-invariant linear systems subject to input and state constraints. It is shown that the recoverable region (which is the largest domain of attraction that is theoretically achievable) can be semi-globally stabilized by continuous nonlinear feedbacks while satisfying the constraints. Moreover, a reduction technique is presented which shows, when trying to compute the recoverable region, that we only need to compute the recoverable region for a system of lower dimension, which generally leads to a considerable simplification in the computational effort.