Observer-Based $H_\infty$ Repetitive Control for Fractional-Order Interval Type-2 TS Fuzzy Systems

This study explores the observer-based $H_\infty$ repetitive control problem for a class of fractional-order systems subject to external disturbances described by an interval type-2 Takagi-Sugeno fuzzy model approach. By combining the Lyapunov method and linear matrix inequalities technique, a tracking control input is designed with a prescribed disturbance attenuation performance level such that all states of the resulting closed-loop control system will be bounded and the tracking error can fluctuate near the origin in a small neighborhood. The main attention of this work is focused on the design of the repetitive tracking controller to asymptotically stabilize the fractional-order nonlinear systems and to achieve $H_\infty$ tracking performance. Precisely, a new set of sufficient conditions is derived in the form of linear matrix inequalities that ensure the desired stability and $H_\infty$ performance, and the controller gain is then computed. Finally, a numerical example is exploited to demonstrate the effectiveness and potential of the proposed control design technique.