Robust Pinning Synchronization of Complex Network with Non-linear Coupling using Switching Control

This paper describes pinning synchronization of a complex dynamical network consisting of N identical nodes. The nodes are interconnected by a time-varying non-linear coupling terms, which has a general type with some constraints. Many non-linear coupling forms can be modeled as the one considered in this work. The network synchronization is achieved by using non-linear switching control. The stability of the synchronization is proven mathematically using Lyapunov analysis. It is shown that the proposed controller performs well in the presence of disturbances. Finally, simulation examples of Lorenz oscillator networks are given to verify the theoretical results. The simulations show that the proposed switching control outperforms classical linear control by providing not only faster synchronization, but also better robustness against external disturbances.