Simultaneous local stabilisation and fault detection for continuous‐time T‐S fuzzy systems

Abstract

In this study, a simultaneous local stabilisation and fault detection (FD) problem for Takagi-Sugeno (T-S) fuzzy systems is investigated. The authors' attention is focused on synthesising an FD observer and an observer-based controller to achieve the objectives of local stabilisation and FD simultaneously. First, by establishing the relationship among the reachable set, the ellipsoid set and the objective area, a new local stabilisation criterion is proposed. The presented criterion guarantees that the state trajectory starting from a given local region can remain in this region even when the system is subject to disturbances and faults. Meanwhile, the FD observer is designed under a mixed framework such that the residual signal is robust to the persistent disturbance and sensitive to the fault. Different from some existing methods, via the proposed scheme, the state can be restricted into the modelling area so that the non-linear control problem can be addressed by the T-S fuzzy model approach effectively. Additionally, two different methods are utilised in the co-design of the observer and the controller such that the disturbance is not required to be energy-bounded. Finally, the effectiveness of the proposed approach is demonstrated by an example.