Abstract: This paper is concerned with state feedback H∞ control for discrete-time polytopic systems by using new Lyapunov function and controller, and the slack variables are introduced for the current time parameter and next time parameter respectively, which is different from other methods by which the variables are introduced only for the current time parameter.The method extends previous one and accelerates the convergence rate, which overcomes drawbacks of previous method that the convergence rate is slow and the degree can not go infinitely, thus leading to less conservative results.In the end, simulation experiments are given to demonstrate the effectiveness of the proposed approach.