This paper investigates the problem of designing a dynamic $mathfrak{H}_{infty}$ output-feedback controller under an $mathfrak{L}_{infty}$ performance representing componentwise input constraints. In order to derive a less conservative stabilization condition therein, this paper introduces a Lyapunov function-based polytopic control law and proposes a method capable of applying the information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as convex polytope. Through this paper, the resultant $mathfrak{H}_{infty}/mathfrak{L}_{infty}$ problem is efficiently solved based on the set invariance condition formulated in terms of linear matrix inequalities (LMIs).