Fixed-Time/Preassigned-Time Synchronization of Multi-Layer Stochastic Complex Dynamic Networks with Intra-Layer Coupling Disturbance
Xiaozhuo Deng, Jing Li, Zhaohui Zhang · 2023
This paper addresses the fixed-time and preassigned-time synchronization of multilayer stochastic complex dynamic networks with intra-layer coupling disturbances. In particular, the node number and topology of each layer can be varied to allow the model to stand for a vast amount of multilayer networks. Based on the Lyapunov stability theory, stochastic differential equations and their stability theory, non-chattering controllers are developed, and sufficient conditions for matrix inequalities are given to realize the fixed-time and preassigned-time synchronization. In addition, it is proved that the network under consideration can achieve synchronization in a pre-specified time, independent of the settling time of the fixed-time synchronization. Finally, the correctness of these theories is confirmed by the numerical simulation of a two-layer network.