This paper investigates 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 semiglobally stabilized by continuous nonlinear feedbacks while satisfying the constraints. Moreover, when trying to compute the recoverable region, a reduction technique shows 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. (C) 2004 Elsevier Ltd. All rights reserved.