This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm the practical exponential stability and design of the proposed class of systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These conditions are expressed in the form of linear matrix inequalities (LMI) which could be solved by using solvers in LMI Toolbox of MATLAB. Two numerical examples are given to illustrate the applicability of the proposed results.

This paper focuses on the Fault-Tolerant Tracking Control (FTTC) design for a PV pumping system using an Induction Motor (IM) drive. This control strategy offsets the effect of the sensor faults and ensures the transfer of optimal power to unit motor–pump. First, to simultaneously estimate the system states and the sensor faults, we developed a Takagi Sugeno (TS) fuzzy descriptor observer. After that, a fault-tolerant controller is synthesized and it is able to track the desired trajectory delivered by a TS fuzzy reference model. The developed control strategy is based on the Lyapunov theory and the H∞ approach, to minimize the disturbances effect. Linear Matrix Inequality (LMI) was solved to calculate the controller and the observer gains. At last, simulations have been done to illustrate the Fault-Tolerant Tracking Control performance of the developed control strategy.

In this paper, robust optimal control of an uncertain wind energy conversion system (WECS), described by a TakagiSugeno fuzzy model, is proposed to guarantee the maximum power trajectory tracking (MPTT). The design of the fuzzy optimal control is based on a quadratic criterion related to the maximum power tracking error. The proposed fuzzy controller allows to regulate the rectified direct current (DC) voltage of the variable-speed wind turbine by adjusting the duty cycle of a boost converter. Linear matrix inequality (LMI) conditions, ensuring the optimal H₂ tracking error, are proposed for the controller gain design. Simulation as well as experimental tests are performed for efficiency evaluation of the established MPPT fuzzy control scheme under variable wind speed conditions.

This paper traits the modeling of a PV pumping system composed of an induction motor (IM) connected to a centrifugal pump and subject to variable solar irradiations. A Maximum Power Point Tracker based on Perturb and Observe (P&O) algorithm is applied for the objective of ameliorating the performance of the pumping system. A Takagi-Sugeno (TS) fuzzy controller, based on a reference tracking TS model, is implemented to the IM. First, A mathematical model in the synchronous d-q frame rotating is developed, that is later converted to a TS model with field-oriented control strategy. After that, basing on the H ^∞ performance, a fuzzy state feedback controller is established to insure the reference trajectory tracking, provided by the TS reference model. The fuzzy observer is applied to estimate the rotor flux which is inaccessible. The control law developed is based on the minimization of the disturbances effect on the tracking error according to the H ^∞ criterion. The control strategy is based on the Lyapunov theorem to guarantee the trajectory tracking performance. Thus, stability conditions, the controller and observer gains are formulated as linear matrix inequalities (LMI). At last, simulation is done to illustrate the tracking performance of the developed T-S tracking controller.

This paper presents a comparison between adaptive input-output linearization and adaptive fuzzy sliding mode control (FSMC) for induction motor. At first, we describe the adaptive linearization control method, which consists in the cancelling of the nonlinearities and decoupling between speed and flux of the system when Rr and TL are unknowns constants. The adaptive sliding mode control, which is insensitive to parameter variations and external disturbances. The substituting of discontinuous control by fuzzy system can be solution for the chattering problem and minimize the control effort.