A Distributed Fault Detection Filter based on Zonotopes

In this paper, a distributed fault detection filter based on zonotopes is proposed for discrete-time distributed systems subject to additive actuator faults. The considered discrete-time distributed systems are also perturbed by unknown-but-bounded uncertainties, including state disturbances and measurement noises. By using zonotopic approaches, the effects of system un-certainties and faults can be divided into two deterministic zonotopes for each subsystem. Based on this decomposition, the distributed fault detection filter gains are designed to be robust against uncertainties and meanwhile sensitive to actuator faults in a finite-frequency domain. As a result, two linear matrix inequality conditions are developed for the design of the distributed fault detection filter gains. Finally, the effectiveness of the proposed approach is shown with some numerical simulations.