This paper presents a new methodology of regional stabilization for a class of uncertain nonlinear systems with input saturation by state feedback. In this approach, nonlinear systems are described by Differential-Algebraic Representations (DAR) and regional stability is guaranteed through a set of conditions in terms of Linear Matrix Inequalities (LMIs) to obtain the largest estimated ellipsoidal Domain of Attraction (DoA) within a given polytopic region in state space. The proposed approach incorporates information about the system's nonlinearities in the control law and uses new auxiliary decision variables in order to achieve less conservative results. Numerical examples illustrate the effectiveness of the proposed methodology, showing favorable comparisons with approaches in a similar context.