Prescribed-time synchronization of undirected and directed matrix-weighted networks

Prescribed-time synchronization in complex networks has garnered significant research attention due to its broad engineering applications. While existing synchronization studies predominantly consider scalar-weighted node interactions, real-world network systems frequently require matrix-weighted representations to accurately capture multidimensional state coupling between nodes. This paper systematically investigates prescribed-time synchronization in matrix-weighted complex networks with both undirected and directed topologies. By constructing a Lyapunov-based analytical framework, we establish rigorous synchronization conditions that guarantee convergence within the prescribed time horizon. Extensive numerical simulations not only validate the theoretical results but also demonstrate the method’s versatility across diverse network configurations. The proposed approach provides a unified control framework with potential applications in power grid synchronization, neural network coordination, and social network dynamics, offering substantial improvements over conventional scalar-weighted network models. • We extend prescribed-time synchronization from scalar-weighted networks to the matrix-weighted case. • We incorporate node-specific dynamics, advancing consensus-based analyses to full synchronization problems. • We rigorously explore the quantitative relationship between the eigenvalues of the Laplacian matrix in matrix-weighted networks and the system’s parameters.