Lower triangle factor based sliding mode observers design for T-S fuzzy systems with faults

The paper mainly focuses on the fault estimation for a class of Takagi-Sugeno (T-S) fuzzy systems with faults. A synthetic estimation observer design method is proposed. The synthetic estimation observer can cover the robust observer, adaptive observer and intermediate estimation observer in the existing study work. Based on the observer design method, an LTF-based sliding mode observer (SMO) is designed for the T-S fuzzy system in consideration. Under the observer, the fault occurring in the system can be well estimated. The obtained LMI-based conditions guarantee the states of the error dynamics to be uniformly ultimately bounded. A numerical example tests the proposed method.