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In this brief, a fault diagnosis (FD) and fault-tolerant control framework is addressed for a class of typical non-Gaussian processes by using two kinds of different fuzzy modeling methods. In order to describe the gray-box dynamics between probability distribution function (PDF) of system output and controlled input, the well-known fuzzy logic systems and the T–S fuzzy models are imported at the same time. Different from some ecumenical results of FD, the PDF of output is assumed to be available rather than output signal itself. By utilizing adaptive projection algorithm, a measurable distribution-based fuzzy diagnostic filter is raised to successfully calculate the state vector and the size of fault. Meanwhile, the dynamical stability of error system can be ensured when non-Gaussian processes exist unknown fault. Moreover, the fault-tolerant controller is provided where not only the diagnostic error but also the system state is retained in a small region. By considering constant and time-varying faults, respectively, a satisfactory simulation result can be achieved to show the effectiveness of designed algorithm. [ABSTRACT FROM AUTHOR]