New fault diagnosis (FD) and fault tolerant control (FTC) algorithms for non-Gaussian singular stochastic distribution control (SDC) systems are presented in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in the FD and FTC design. The proposed approach relies on an iterative learning observer (ILO) for fault estimation. The fault may be constant, fast-varying or slow-varying. Based on the estimated fault information, the fault tolerant controller can be designed to make the post-fault probability density function (PDF) still track the given distribution. Simulations are given to show the effectiveness of the proposed FD and FTC algorithms. (C) 2012 Elsevier Ltd. All rights reserved.