Fault Detection for Singular Discrete-Time Linear Systems with Signal-to-Noise Ratio Constrained Channels

Abstract

This paper deals with the fault detection problem for singular discrete-time linear systems with additive white Gaussian noise channels subject to signal-to-noise ratio constraints. An observer-based fault detection scheme which consists of residual generator, threshold and false alarm rate is constructed. In the proposed scheme, the design of residual generator is realized in the context of $${H_\infty }$$Hź-filtering problem when the fault and unknown disturbance are present, and the estimations of both system state and fault are obtained in the design procedure. Then, in order to detect the fault, an online threshold based on the stochastic characteristics of channel noise is established. For the purpose of evaluating the fault detection system performance, the false alarm rate is guaranteed to be below a certain level. Finally, a simulation example is exploited to illustrate the application and effectiveness of the proposed method.