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In this paper, a new optimal fault-detection (FD) problem is addressed for a class of non-Gaussian stochastic systems called stochastic distribution systems (SDSs). For an SDS, the available information for the FD system may be the measured output probability density function. A sufficient existence condition of guaranteed cost filters is presented by constructing an augmented Lyapunov functional approach. In order to improve the detection sensitivity performance, an optimization algorithm, with linear matrix inequality constraints, is presented to minimize the threshold value. An example is given to demonstrate the effectiveness of the proposed approach.