This paper focuses on the stabilization problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimization problems with LMI constraints are therefore proposed to compute stabilizing state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results.