Lag synchronization for time-delayed chaotic systems via the H _∞ approach

This paper proposes a new H_∞, lag synchronization scheme for time-delayed chaotic systems with external disturbance. Based on Lyapunov-Krasovskii stability theory, the H_∞ lag synchronization controller is presented such that the time-delayed lag synchronization error system is asymptotically stable with a guaranteed H _∞ performance. It is shown that the design of the proposed lag synchronization controller can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The lag synchronization problem for time-delayed chaotic Hopfield neural networks is provided to demonstrate the effectiveness of the developed theoretical results.