Observer-based finite-time control of conformable Takagi–Sugeno fuzzy systems with time delay

This paper examines finite-time (F-T) observer-based control of fractional-order nonlinear systems with time delay, employing the Takagi–Sugeno fuzzy (T-SF) approach. This study utilizes the conformable fractional derivative (CFD) as its foundational framework. Sufficient conditions are formulated to guarantee that the augmented vector, consisting of the state estimates and the state estimation errors, stays within a ball centered at the origin. This applies not only to specified initial conditions but also to predefined disturbances. These conditions are then reformulated as linear matrix inequalities (LMIs) conditions, which can be efficiently solved using the LMI toolbox. An illustrative example is given to illustrate the proposed result.