Fault Detection Approach for Nonlinear Systems via Nonlinear Factorization and Fuzzy Models

This brief aims to propose an effective fault detection method for general class of nonlinear systems in the context of the closed-loop system stability. To this end, the nonlinear factorization technique is first used to model the faulty nonlinear systems, which can be represented by the so-called stable kernel representation with a stable parameterization of the system changes triggered by faults. Then, the closed-loop system stability is discussed according to the internal stability definition and the small gain theorem, respectively, to present the design framework of the fault detection system. Different from the traditional fault detection schemes, the proposed fault detection approach focuses on detecting whether the system closed-loop stability is damaged by faults utilizing the online measurable system and controller residual signals. Furthermore, for the implementation of the proposed fault detection framework, Takagi-Sugeno fuzzy models are applied to approximate the nonlinear systems and thus the fault detection system design methods can be provided by taking advantage of the linear matrix inequality technique. Finally, a case study is used to verify the achieved results.