This paper is concerned with the controller synthesis for feedback systems with saturation based on the LPV system representation. The LPV system representation, combined with use of the detailed structure of saturation nonlinearity, enables us to reduce the conservativeness. In this paper, we develop a new iterative algorithm for designing a linear time-invariant controller which locally stabilizes the nonlinear closed-loop system and achieves the prescribed quadratic control performance. The present design method provides an explicit expression for a guaranteed domain of attraction, and maximizes the estimated region of the plant states for which the stability and the prescribed quadratic performance are satisfied. A numerical example shows the effectiveness of the present design method.