Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control

This paper investigates the exponential synchronization problem of nonlinear complex dynamical systems via delayed impulsive distributed control. Different from the existing results on the synchronization of complex dynamical systems, impulsive input delays are considered in our model. Combined with the time-varying Lyapunov functional and mathematical induction approaches, criteria on system synchronization are established, which sufficiently utilize the information of both the state variables of themselves and their neighbors. Moreover, it is shown that the frequency of impulsive occurrence and impulsive input delays can heavily affect the synchronization performance. Finally, two numerical simulations are given to illustrate the effectiveness of the derived theoretical results.