This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we design a robust observer-based controller for the obtained fuzzy system by utilizing the differential mean value approach. The observer and controller gains are obtained by the separation principle, in which the problem is solved in the sum of linear matrix inequalities (LMIs). The paper presents two main contributions: A state feedback controller is designed using differential mean value (DMVT) which ensures robust stabilization of the nonlinear system. Additionally, the Luenberger observer is extended to the Takagi–Sugeno fuzzy models. The second contribution is to reduce conservatism in the obtained conditions, a non-quadratic Lyapunov function (known as the line integral Lyapunov fuzzy candidate (LILF)) is employed. Two examples are provided to further illustrate the efficiency and robustness of the proposed approach; specifically, the Takagi–Sugeno fuzzy descriptor of an induction motor is derived and a robust observer-based controller applied to the original nonlinear system.

Induction motors are extensively utilized across industries due to their robust efficiency, versatility, and cost-effectiveness, necessitating the precise parameter estimation of their equivalent circuit for effective operation and maintenance

The growing significance of photovoltaic (PV) monitoring systems and diagnostic methodologies is evident in their role in enhancing the power generation, efficiency, and durability of photovoltaic systems. The operational efficacy of these systems is primarily influenced by factors such as irradiation levels and cell temperature. Consequently, there exists a pressing need for dedicated scrutiny and scholarly investigation into the identification and diagnosis of defects within these systems, aiming for swift identification and rectification of failures in PV stations. This paper thus endeavors to introduce a diagnostic methodology focused on fault detection and categorization of eight types of faults occurring in shading, series resistance, shunt resistance, and bypass diode faults (disconnected, short circuited, shunted with resistor) within photovoltaic panels. This analysis employs two distinct algorithms: the initial algorithm employs the thresholding method, while the second algorithm is grounded in a Fuzzy Logic classifier (Sugeno model). Upon examination of the simulation outcomes, it becomes evident that the threshold method fails to identify all faults, necessitating the adoption of a more effective classification technique. Moreover, the Fuzzy Logic (FL) method has proven to be the most suitable approach for diagnosing PV module issues. The findings indicate that all specified faults are detectable in a discernible manner. These approaches have demonstrated proficient accuracy and efficacy in pinpointing and characterizing various faults within PV panels. Notably, our simulation endeavors were conducted utilizing Simulink/Matlab software (R2014a).