This article deals with the stabilization of constrained linear systems and state-space linearizable nonlinear systems and the estimation of regions of closed-loop stability. To this end, linear and linearizing static state feedback control laws are considered and a methodology to design their gains is presented. The resulting closed-loop system is such that it can be transformed, via a change of variables, into a form that facilitates the estimation of regions of stability without having to resort to a Lyapunov stability analysis. The desirable features of this approach are its ease of implementation and its relative non-conservativeness over a Lyapunov-based approach; these are illustrated by applying the theory to various examples.