A unified finite-/fixed-time synchronization approach to multi-layer networks

This brief investigates synchronization of multi-layer networks by a new unified finite-/fixed-time (FTT/FXT) control approach. First, a new unified FTT/FXT stability theorem of dynamical system is proposed. Second, novel sufficient criteria are gained for FTT/FXT synchronization of multi-layer networks by using the continuous controller or the discontinuous controller. In particular, a new unified framework for FTT/FXT synchronization of multi-layer networks is given, and the relationship between the minimum FTT/FXT and the number of network layers is also established, which can be helpful to select appropriate parameters in practical control. Finally, numerical simulations are given to verify the effectiveness of the proposed method.