Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes

This paper deals with the pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delays and time-varying delays in the dynamical nodes. We control a part of the nodes of the complex networks by using adaptive feedback controllers and adjusting the time-varying coupling strengths. Based on the Lyapunov--Krasovskii stability theory for functional differential equations and a linear matrix inequality (LMI), some sufficient conditions for the synchronization are derived. A numerical simulation example is also provided to verify the correctness and the effectiveness of the proposed scheme.