One of the fundamental topics in engineering that has many applications in applied sciences is guaranteed cost control and synchronization of chaotic dynamical systems. In this paper, a Takagi–Sugeno (T-S) fuzzy model-free state feedback (MFSF) technique is used to synchronize and stabilize various complex fractional-order systems (FOSs) in the presence of input saturation. A T-S fuzzy MFSF method is developed to suppress the inappropriate behavior of the FOSs without any unpleasant chattering phenomena using the non-integer form of the Lyapunov stability theory (LST) and linear matrix inequality concept. The suggested MFSF technique may be used to stabilize and synchronize FOSs with model uncertainty, external disturbances, and input saturation. The designed method has the advantages of being a model-free technique, being resistant to uncertainties, being simple to use, and achieving the equilibrium point quickly at a guaranteed cost. Furthermore, the effectiveness and application of the T-S fuzzy MFSF are proven using the suggested approach to synchronize two separate canonical chaotic FOSs and stabilize the permanent magnet synchronous motor (PMSM) chaotic system. Two comparisons demonstrate the efficacy and advantages of the T-S fuzzy approach over other existing control methods.

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