Local exponential synchronization in complex dynamical networks with time-varying delay and hybrid coupling

In this paper, the local exponential synchronization of complex dynamical networks with time-varying delay and hybrid coupling is investigated. We assume that the coupling configuration matrices are asymmetric and the inner coupling matrices are not restricted to be diagonal or positive definite. Through constructing the appropriate Lyapunov–Krasovskii functional and applying the linear matrix inequality (LMI) technique, several novel delay-depend sufficient conditions and the decay rate are deduced for the local exponential synchronization. Moreover, the derivative of the time-varying delay is extended to any value. Finally, the numerical simulations are given to show the effectiveness of the theoretical results.