Open AccessSimultaneous local stabilisation and fault detection for continuous‐time T‐S fuzzy systems
Author(s) -
Wu Yue,
Dong Jiuxiang
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.6124
Subject(s) - control theory (sociology) , observer (physics) , ellipsoid , residual , fault detection and isolation , fuzzy logic , computer science , bounded function , controller (irrigation) , state observer , trajectory , mathematics , control (management) , nonlinear system , algorithm , artificial intelligence , actuator , mathematical analysis , physics , quantum mechanics , astronomy , agronomy , biology
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 L ∞ / H _ 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.