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In this work, a new technique for the computation of ellipsoidal invariant sets for continuous-time linear systems controlled by a saturating linear control law is presented. New sufficient conditions to guarantee that an ellipsoid is a contractive invariant set for the closed-loop system is presented. The contractive nature of the invariant set ensures asymptotic stability of the controlled system. The main contributions of the paper are the following: the proposed sufficient condition is expressed in form of linear matrix inequalities constraints. The presented method includes (and consequently improves) previous results on this topic. The computational complexity of the proposed approach is analyzed. Illustrative examples are given.