Prescribed-time cluster synchronization of uncertain complex dynamical networks with switching via pinning control

This paper focuses on the cluster synchronization problem in the prescribed-time of a class of uncertain complex dynamical networks with switching signal which is characterized by average dwell-time constraint. Different from traditional complex dynamical networks, uncertainties, switching signals and nonlinear coupled properties have been introduced to the networks. By applying switched system theory and matrix decomposition method, conditions have been established to ensure that such complex dynamical networks can achieve the desired performance in finite time which is given in advance. Additionally, the methods and results about prescribed-time stable issue of switched systems can be employed to other more general systems. Finally, one numerical example is presented to show the effectiveness of the theoretical results.