The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter(FDF) as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method. The problem of fault detection for linear discrete time varying systems with multiplicative noise is dealt with. By using an observer-based robust fault detection filter (FDF) as a residual generator, the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems. A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation. The determination of the parameter matrices of the filter is converted into a quadratic optimization problem, and an analytical solution of the parameter matrices is obtained by solving the Riccati equation. Numerical examples are given to illustrate the effectiveness of the proposed method.