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This study deals with the problem of H∞ fault detection for linear discrete time-varying systems with delayed state in the framework of H∞ filtering. The design of the H∞ fault detection filter (FDF) is firstly converted into the minimum problem of an indefinite quadratic form. After introducing a corresponding Krein space stochastic system and building a relationship with projection, a sufficient and necessary condition on the existence of the minimum is derived by applying innovation analysis. A solution to the H∞-FDF is obtained in terms of matrix difference equations. Numerical examples are given to demonstrate the effectiveness of the proposed method.