DELAYED FEEDBACK $\mathcal{H}_{\infty}$ SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS BASED ON T–S FUZZY MODEL

In this letter, we propose a new $\mathcal{H}_{\infty}$ synchronization method, called a delayed feedback fuzzy $\mathcal{H}_{\infty}$ synchronization (DFFHS) method, for time-delayed chaotic systems with external disturbance. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the DFFHS controller is presented to not only guarantee aymptotical synchronization but also reduce the effect of external disturbance to an $\mathcal{H}_{\infty}$ norm constraint. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed DFFHS method.

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