Synchronization analysis of a complex network family

This paper is concerned with a meaningful and challenging problem: Is it possible to establish synchronization criteria for a network family, the members of which have different network structure? Based on the parameter-dependent Lyapunov function, some synchronization criteria are proposed to address this problem. These simple yet generic criteria can lead to the advantage of easy synchronization verification of every member from the network family. On the other hand, the problem mentioned above can be regarded as a synchronization problem for a network with structure uncertainty, which is also investigated in this paper. Numerical examples are given to demonstrate the effectiveness of the derived criteria.