Pinning synchronization of fractional-order complex networks with Lipschitz-type nonlinear dynamics

- A fractional-order nonlinear complex network with directed topology is constructed.
- A novel frequency domain approach is developed to analyze synchronization behavior.
- We provide an easily testable criterion for global pinning synchronization.

This paper deals with pinning synchronization problem of fractional-order complex networks with Lipschitz-type nonlinear nodes and directed communication topology. We first reformulate the problem as a global asymptotic stability problem by describing network evolution in terms of error dynamics. Then, a novel frequency domain approach is developed by using Laplace transform, algebraic graph theory and generalized Gronwall inequality. We show that pinning synchronization can be ensured if the extended network topology contains a spanning tree and the coupling strength is large enough. Furthermore, we provide an easily testable criterion for global pinning synchronization depending on fractional-order, network topology, oscillator dynamics and state feedback. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.