A New Lyapunov Function Method to the Fixed-Time Cluster Synchronization of Directed Community Networks

In this paper, the issue of fixed-time cluster synchronization is investigated for the directed community networks. We propose a new Lyapunov function method which leads to the settling time is not only independent of the initial value, but also unrelated to the number and dimensions of nodes in the networks. This means our estimated settling time is more accurate and much tighter than the one in the existing results. By designing the corresponding controllers and using the fixed-time stability theorem, some new criteria are derived to guarantee that the community networks achieve cluster synchronization in fixed time. Finally, an illustrative example with computer simulations is given to verify the theoretical analysis.