While the \(H_\infty \) observer-based control has found widespread application in the literature for integer-order systems, researchers have shown less interest in addressing the same issue within the fractional-order framework. In this context, this study delves into the application of \(H_\infty \) observer-based control for the Hadamard fractional-order system (HFOS) described by the Takagi–Sugeno fuzzy models (TSFM). Using Lyapunov approach and by employing a matrix decoupling technique, LMI based conditions ensuring the existence of an observer and controller, are proposed. To minimize the impact of disturbances on the controlled output, \(H_\infty \) optimization technique is used. The validity of our approach is substantiated through an example, underscoring the robustness and reliability of our proposed findings.
