Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller

In this paper, an integral sliding mode control approach is presented to study the projective synchronization for different chaotic time-delayed neural networks. A sliding mode surface is appropriately constructed and a sliding mode controller is synthesized to guarantee the reachability of the specified sliding surface. The global asymptotic stability of the error dynamical system in the specified switching surface is investigated with the Lyapunov–Krasovskii (L–K) functional method. A delay-dependent sufficient condition is derived and the maximum time-delay value is obtained by means of the linear matrix inequality (LMI) technique. A simulation example is finally exploited to illustrate the feasibility and effectiveness of the proposed approach, verify the conservativeness of L–K method and LMI technique, and exhibit the relationship between the convergence velocity of error system and the gain matrix.