Robust Fault Diagnosis for Uncertain Linear Systems: A Set-Based Geometric Approach

This article investigates the robust fault diagnosis problem for uncertain linear systems, where the system uncertainties are represented by interval matrices and there exist bounded disturbances and noises. The original geometric approach requires a precise model of the system, which is no longer satisfied in uncertain systems. Aiming to address this challenge, we make use of the set theory to modify the original geometric approach and propose a new set-based fault observer to achieve robust fault detection and isolation (FDI) for uncertain linear systems. In addition, we propose a novel fault estimator to estimate fault based on the set-based geometric approach as well. In this article, we take advantage of zonotopes to describe the range of variables and adopt
$F_{W}$
-radius as the index to indicate the zonotope size. By optimizing this index, we calculate the optimal observer parameters to obtain better diagnosis performance. A numerical simulation is presented to illustrate the advantages of the proposed robust fault diagnosis scheme.