Stabilization of polynomial systems is revisited in this paper. Here, we proposed a new sufficient condition for the controller design, with guaranteed bounds on the input magnitudes. In the proposed synthesis condition, the system matrices and the Lyapunov matrices are separated, and hence parameterization of the resulting controller is independent of the Lyapunov matrices. Moreover, the proposed condition is convex in the decision variables and solvable via the sum-of-squares (SOS) technique. Main contributions of the proposed approach are twofold. Firstly, parameter-dependent Lyapunov functions can be considered in robust controller design for uncertain polynomial systems. Secondly, static output-feedback design can be addressed in a computationally efficient manner.