Conservatism Comparison of SUIO and Luenberger Observer in Invariant Set-Based Robust Fault Detection for LPV Systems

This paper concentrates on analyzing and comparing the invariant set-based fault detection (FD) performance of the set-theoretic unknown input observer (SUIO)-based method and the Luenberger observer (LO)-based method for discrete-time linear parameter varying (LPV) systems. We aim to systematically compare their FD performance under a set-theoretic framework. First, the quadratic H
∞
stability conditions of the state-estimation error dynamics are respectively established for the two FD methods. Then, for the purpose of characterizing the FD performance mathematically, a practical construction approach of the invariant sets for the dynamics with convex polytopic form is presented. Finally, an effective comparison criterion of the FD conservatism of the SUIO-based method and the LO-based method is obtained by using the Frobenius norm-based sizes of residual zonotopes. A vehicle example is utilized to illustrate the effectiveness of the obtained results.