$${L_\infty }$$ Fault Estimation and Fault-Tolerant Control for Nonlinear Systems by T–S Fuzzy Model Method with Local Nonlinear Models

Abstract

This paper investigates the problems of the observer-based fault estimation (FE) and fault-tolerant control (FTC) for nonlinear systems subjected to external disturbances by the T–S fuzzy model method with local nonlinear models. Firstly, an FE strategy is proposed based on the unknown input observer technology, where the local nonlinear terms can be decoupled from the FE error system for relaxing the design of observer. Then, by using the FE information, a fuzzy fault-tolerant controller is designed to guarantee the stability of the system. Additionally, in the design schemes of the FE observer and the fault-tolerant controller, the $${L_\infty }$$ method is used to deal with the problems of FE and FTC for the system with persistent disturbance such that the robustness of the system against the persistent external disturbance can be increased. Compared with the traditional $${H_\infty }$$ method which is only applicable for dealing with the energy bounded signals, the $${L_\infty }$$ FTC strategy proposed in this paper can deal with the persistent disturbance such that the shortcomings of the traditional $${H_\infty }$$ approach are overcome. Finally, the effectiveness of the proposed method is verified by simulation results.