This article presents new stabilization conditions for the state feedback control of switched linear systems subject to actuator saturation. Based on the semiellipsoidal approach and the multiple Lyapunov functions method, state feedback controllers and a state-dependent switching law are designed. The presented stabilization conditions are less conservative than those obtained by the ellipsoidal method and simpler than those established by the polyhedral method. Moreover, the union of all positively invariant semiellipsoids is constructed to approximate the region of attraction. Each semiellipsoidal set is the intersection of a positively invariant ellipsoidal set and a constraint set. Constructive solutions of the presented conditions are obtained based on two different techniques: the sum-of-squares technique and the nonlinear matrix inequality technique. Two illustrative examples are given to demonstrate the effectiveness of the main results.