Fast Fixed-Time Control for Intra- and Inter-Layer Synchronization of Multi-Layer Networks

This study addresses the problem of fast fixed-time synchronization (FDTS) in multi-layer networks (MLNs), focusing on both intra-layer and inter-layer dynamic synchronization. First, we propose a more representative MLN framework in which each layer has a distinct topological structure, and node-to-node connections are established between corresponding nodes across layers. Second, we design a fast fixed-time controller to achieve synchronization of MLNs and estimate the synchronization time. Third, by applying the Lyapunov method and comparison theorem, we derive several novel synchronization conditions that are independent of initial states. Finally, numerical simulations are conducted to validate the theoretical findings.