Slim . Dhahri

For classical integer-order systems, the task of designing observers that are both robust and non-fragile has attracted much attention in the literature. It's worth noting that little research has been done on non-integer-order systems. It has been shown that there is a way to create robust observers in Lipschitz Caputo-Hadamard fractional order systems. As a result, the H_\infty\ performance technique is used to achieve this. In a numerical example, simulations confirm the effectiveness of the proposed method.

In this project, we will discuss the problem of finite time stability (FTS) for Caputo–Hadamard fractional differential system with uncertainties. New sufficient conditions are derived by employing Lyapunov stability theory, and expressed in terms of LMIs. Some results are obtained to confirm the validity of the proposed approach.

In this project, we will discuss the observer design problem for Caputo–Hadamard fractional differential system in terms of Mittag–Leffler functions. The proposed observer guarantees that the estimation error is uniformly bounded. We will establish some new sufficient conditions for practical stability using Mittag-Leffler terms. In addition, some applications confirm the validity of the obtained results.

In this project, we will study the problems of robust fault estimation (FE) and fault-tolerant control (FTC) for the premise variables (PVs) unmeasured T-S fuzzy systems affected by external disturbances, actuator and sensor faults. We will design a fuzzy adaptive sliding mode observers (SMOs) with estimated PVs to estimate the system states and faults. We will develop a dynamic output feedback FTC (DOFFTC) to stabilize the resulting closed-loop systems. We will establish new sufficient conditions for the existence of the proposed observers and controllers.