This paper considers a nonlinear feedback control policy that is an extension of those provided by command governors and reference governors. As in these control approaches it applies to discrete-time linear systems with hard constraints and set bounded disturbances. The control policy retains the main properties of traditional governors, such as straightforward direct implementation and finite-settling-time response to arbitrarily specified set points. Its principal advantage over traditional governors is a significantly larger domain of attraction, that may compete in size with those obtained by dynamic programming. Connections to model predictive control are made. Numerical examples illustrate advantageous features of the proposed approach. (C) 2010 Elsevier Ltd. All rights reserved.