Abstract: The problem of robust and non-fragile H∞ control for a class of descriptor discrete interval systems with nonlinear disturbance was studied, where the nonlinear disturbance satisfies the Lipschitz condition. First of all, based on the theory of Lyapunov function, the robust H∞ control problem of the uncertain nonlinear descriptor system was described; Secondly, a sufficient condition for the existence of robust and non-fragile H∞ controller was given by linear matrix inequality approach, which guarantees that the resulting closed-loop descriptor system is admissible and satisfies a prescribed H∞ norm-bounded constrain for all admissible uncertainties. Meanwhile, the design method of the state feedback controller was proposed. Finally, numerical simulation results indicated the effectiveness of the developed method.