Distributed Fault Detection for Linear Time-Varying Multi-Agent Systems With Relative Output Information

This paper investigates the distributed fault detection problem for linear discrete time-varying heterogeneous multi-agent systems under relative output information. Due to the lack of absolute outputs, an augmented model is built by stacking all local relative output information. Then, the fault detection problem consisting of residual-generation and residual-evaluation is handled using the $H_{\infty }$ filtering framework. The residual-generation problem is actually a minimization problem of an indefinite quadratic form, and the Krein space-Kalman filtering theory is applied, which results in a low computational burden despite the time-varying characteristic. Using the Krein space theory, a necessary and sufficient condition for the minimum is derived, and a residual-generation algorithm is developed. Further, a residual-evaluation mechanism is designed by constructing an evaluation function and detecting faults by comparing it with a threshold. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed fault detection approach.