Synchronization time and energy consumption for multiweighted complex networks

Abstract

This paper investigates finite-time, fixed-time, and prescribed-time synchronization of multiweighted complex networks (MCNs) with an emphasis on balancing synchronization time and energy consumption. For finite-time and fixed-time synchronization, the upper bounds for both synchronization time and energy consumption are estimated, with the fixed-time controller offering a settling time (synchronization time) that is independent of the network's initial state. To improve the accuracy of energy estimation, we first use the general p-th power form instead of the commonly used square form. These estimations of synchronization time and energy consumption are then normalized and balanced in a performance evaluation function. Both theoretical and numerical results reveal optimal control gain values, aiding in parameter selection to minimize this performance function. For prescribed-time synchronization, we estimate energy consumption through the exponential integral. To address the challenge of multiple weights, we apply the rearranging variables' order technique (ROT). Using normalized left eigenvectors associated with zero eigenvalues of union matrices after ROT, we construct a Lyapunov function that yields new synchronization criteria for MCNs. Numerical simulations confirm the theoretical findings, demonstrating synchronization under the derived conditions and a clear balance between synchronization time and energy consumption.