This paper focuses on the fault detection of a class of discrete-time systems with random faults and proposes a fault-dependent approach. Firstly, a mathematical model is constructed to describe the above problems, and the characteristics of fault signals are transformed into matrices containing uncertainties. By constructing a fault detection filter as a residual generator, the fault detection and isolation (FDI) problem is transformed into a H_∞filtering problem. Based on the established model, the  H_∞ performance is analyzed by adopting a fault-dependent method. The parameter-dependent Lyapunov function is selected for processing. On this basis, the existence condition of the fault detection filter is given in the form of linear matrix inequalities. Finally, an example is used to verify the effectiveness and practicability of the theoretical results.