Robust Fault Estimation and Fault-Tolerant Control for a Class of Fuzzy Singularly Perturbed Systems With State Time Delay Based on Learning Observer

Abstract

This article studies the problem of fault estimation (FE) and dynamic output fault-tolerant control (DOFTC) for a class of Takagi–Sugeno (T–S) fuzzy singularly perturbed systems (SPSs) which subject to time delay, external disturbance and actuator fault. A new fault estimation and fault-tolerant control scheme was proposed and designed for the influence of the change of perturbation parameter $\epsilon$ on the singularly perturbed system. This scheme adopts the Takagi–Sugeno (T–S) fuzzy model, learning observer and dynamic output feedback fault-tolerant mechanism, so that the system has multi-time-scale dynamic stability. The results show that this method has more accurate estimation effect, faster convergence speed, and very fast steady-state response of fault-tolerant control when faults occur. Furthermore, when constructing the Lyapunov function, the improved matrix $P\left(\epsilon \right)$ was selected to ensure that the closed-loop system is stable for all $\epsilon \in (0,\bar{\epsilon }]$, and at the same time, the conservativeness of the results was reduced. Finally, the feasibility and correctness of the proposed design method were illustrated through two numerical examples.