In this paper, we propose a new adaptive $\mathcal_{\infty}$ synchronization strategy, called an adaptive fuzzy delayed feedback $\mathcal_{\infty}$ synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback $\mathcal_{\infty}$ control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed $\mathcal_{\infty}$ performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.