Khalida Mimoune

Fault occurrence in practical systems, if not addressed, can cause diminished performance or even system breakdown. Therefore, fault detection has emerged as a crucial challenge in ensuring system safety and reliability. This paper presents a novel fuzzy observer aimed at reconstructing actuator and sensor faults in nonlinear systems, even when subjected to external disturbances. The approach we propose utilizes the Takagi-Sugeno fuzzy model and Lyapunov function. Initially, by filtering the system output, we construct a system where actuator faults correspond to the original actuator and sensor faults. Subsequently, the impact of disturbance on state estimations is minimized by employing the H-infinity performance criteria. We demonstrate that, for non-disturbed systems, these estimations gradually converge to their true values. In designing the observer gains, transformation matrices are derived by solving linear matrix inequalities. Our approach boasts some advantages over existing methods. By assuming that the premise variables are immeasurable, we enhance the usability of our approach. As a proof of concept, we evaluate two practical systems. The simulation results underline the benefits of our proposed method in terms of rapid and accurate fault detection performance.

This paper is concerned with the stability and stabilization problem of a Takagi-Sugeno fuzzy (TSF) system. Using a non-quadratic function (well-known integral Lyapunov fuzzy candidate (ILF)) and some lemmas, new sufficient conditions are established as linear matrix inequalities (LMIs), which are solved with a stochastic fractal search (SFS). The main advantage of the technique used is its small conservatives. Motivated by the mean value theorem, a state feedback controller based on a non-quadratic Lyapunov function is designed. Unlike other approaches based on poly-quadratic Lyapunov candidates, stability conditions of the closed loop are obtained in LMI regions. It is important to highlight that the time derivatives of membership functions do not appear in the used line integral Lyapunov function, which is the well-known problem of poly-quadratic Lyapunov functions. A numerical example is given to show the advantages and the utility of the integral Lyapunov fuzzy candidate, which provides a wider feasibility region than other Lyapunov functions.