Iterative Interval Estimation-Based Fault Detection for Discrete Time T–S Fuzzy Systems
Mouquan Shen, Tu Zhang, Zheng‐Guang Wu, Qing‐Guo Wang, Song Zhu
Abstract
This article investigates fault detection (FD) for discrete-time T–S fuzzy systems via an iterative interval estimation method. By means of system output and the iterative estimation of unknown disturbances, two iterative subsystems are employed to establish iterative state reconstruction free of faults. Resorting to a structure separation technique and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> requirement imposed on estimated errors, a sufficient condition is formulated in terms of linear matrix inequality to guarantee the asymptotically stability of the error systems. With the help of the zonotope reachability technique, the state interval without faults consideration is rebuilt in terms of the error boundary. Subsequently, an FD scheme is proposed by checking residual signals whether exceed the residual interval generated from the established error interval. Simulation comparison is provided to verify the validity of the proposed iterative FD scheme.