## Synchronization of a delayed complex dynamical network with free coupling matrix.(English)Zbl 1253.93066

Summary: This paper considers a synchronization problem of a delayed complex dynamical network. For the problem, the virtual target node is chosen as one of nodes in the complex network. It should be pointed out that only one connection is needed between a real target node and a virtual target node instead of $$N$$ connections. Moreover, the proposed synchronization scheme does not require additional conditions for coupling matrix unlike the existing works. Based on Lyapunov’s stability theory, a new design criterion for an adaptive feedback controller to achieving synchronization between the real target node and all nodes of the delayed complex network is developed. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

### MSC:

 93C40 Adaptive control/observation systems 34D06 Synchronization of solutions to ordinary differential equations 93A14 Decentralized systems 93C15 Control/observation systems governed by ordinary differential equations
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### References:

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