Abstract: This paper is concerned with the reliable H∞ filtering problem against sensor failures for a class of discrete-time systems with sector-bounded nonlinearities. The resulting design is that the filtering error system is asymptotically stable and meets the prescribed H∞ norm constraint in normal case as well as in sensor failure case. Sufficient conditions for the existence of the filter are obtained by using appropriate Lyapunov functional and linear matrix inequality (LMI) techniques. Moreover, in order to reduce the design conservativeness and get better performance, we adopt the slack variable method to realize the decoupling between the Lyapunov matrices and the system dynamic matrices. A numerical example is provided to demonstrate the effectiveness of the proposed designs.