Synchronization for non-dissipatively coupled time-varying complex dynamical networks with delayed coupling nodes

This paper investigates the synchronization problem for the non-dissipatively coupled time-varying complex dynamical networks via decentralized state feedback controllers. In our network model, the outer coupling configuration matrices are not restricted by dissipatively coupled condition, time invariance, symmetry, irreducibility or certainty. Besides, different time-varying coupling delays are put into consideration. Moreover, the similarities possessed by the nodes in our network model are revealed based on the nodes' dynamics and are applied to synthesize the controllers. Furthermore, it is the common bound, not the exact information, of the outer coupling coefficients that is used to design the synchronization controllers. It is worth pointing out that the uncertain outer coupling coefficients' common bound is admissible in our synchronization schemes, and for this case, adaptive control mechanism is introduced to design the synchronization controllers. Several proper simulation examples are given to verify the effectiveness and feasibility of our theoretical results.