This paper investigates interval estimation for discrete- time nonlinear systems described by polytopic models with measurable premise variables. By assuming that the disturbances and measurement noise are unknown but bounded, an interval observer design is proposed and sufficient convergence conditions are given by Lyapunov stability analysis. To improve the accuracy of interval estimation in order to attenuate energy-bounded unknown inputs such as disturbances, a direct method based on H_∞ approach and pole placement constraints is developed. A numerical example is given to show the effectiveness of the proposed methodology.