An Improved Zonotopic Approach Applied to Fault Detection for Takagi–Sugeno Fuzzy Systems

In this work, an actuator fault detection problem for discrete-time Takagi–Sugeno fuzzy systems is tackled in a bounded error context where both state disturbances and measurement noise are assumed to be unknown but bounded with known bounds. First, a peak-to-peak performance synthesis method is applied to design a robust residual generator against the considered process disturbances and measurement noise. Meanwhile, an improved zonotopic approach is proposed to compute tight adaptive thresholds for residual evaluation. Then, a reliable set-membership fault detection strategy with the aid of generated residual signals and adaptive thresholds is introduced. Finally, the viability of the proposed method is demonstrated via a numerical simulation. Then, an experimentation on a 3-D Crane system is performed to show its practicability.