Finite/Fixed-Time Synchronization of Multi-Layer Networks Based on Energy Consumption Estimation

This paper discusses finite/fixed-time (FNT/FXT) synchronization of multi-layer networks based on energy consumption estimation. Firstly, a novel FXT stability theorem of dynamical system is presented. Secondly, sufficient criteria for FNT/FXT synchronization in multi-layer networks are given, and the estimation of the energy consumption are also gained. Especially, the range of the number of layers of network is gained based on the least convergence time and the estimation of the least energy consumption. The results show that shorter synchronization time and less energy consumption does not mean less network layers. Finally, the validity of the theoretical method is verified by numerical simulation.