Sampled-Data $$H_{\infty }$$ H ∞ Synchronization of Chaotic Lur’e Systems with Time Delay

Abstract

This paper deals with the problem of robust H ∞ synchronization of chaotic Lur'e systems with time-varying delays via sampled-data control. In order to make full use of the information about sampling intervals, nonlinear functions and time-varying delays, an improved Lyapunov-Krasovskii (L-K) functional is introduced. Based on reciprocal convex combination technique, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic synchronization of the considered Lur'e system with a guaranteed H ∞ performance. By solving the obtained LMIs, the required sampled-data control gain matrix is obtained, which assures the asymptotic stability of the error system and reduces the effect of external disturbance according to H ∞ norm. Finally, the effectiveness and less conservatism of the proposed method are verified through numerical simulations of the Chua's circuit and neural networks.

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