An [formula omitted] non-fragile fault detection observer design for discrete-time Takagi–Sugeno fuzzy systems using zonotopic method

Abstract

In practical engineering applications, as the system becomes complex, the need to ensure its safety and reliability increases, and fault detection technology is the key to determining whether it usually operates. The assumption of precise realization implicit in the design of conventional observers is a significant reason why actual fault detection observers find it difficult to detect faults accurately. False alarms can quickly occur during fault detection due to the observer’s uncertainty. For this reason, a novel fault detection method using zonotopic analysis based on a non-fragile H∞ observer via T-N-L structure is proposed for the discrete-time Takagi–Sugeno (T-S) fuzzy system. The observer proposed in this paper is designed in a two-step form. Firstly, the H∞ technique gives a set of design conditions for the fault detection observer with T-N-L structure, which maintains the robustness of the observation dynamics to disturbances while considering the uncertainties existing in the actual observer. Then, the dynamic fault detection thresholds in the form of intervals are given by zonotopic analysis, which has the advantage of zero false alarm rate when the observer parameter ingress is within the range of design considerations. Simulation results show that the method proposed in this paper provides better safety and reduces the problem of missed false alarms compared with the traditional method. It also reflects that the nature of a non-fragile fault detection observer is a trade-off between safety and speed of fault detection.