Finite-Time Synchronization Control for Multi-layer Networks via Energy Estimation

This paper investigates the finite-time synchronization control of multi-layer networks and the associated energy consumption. Firstly, based on finite-time stability theory, a finite-time control strategy is proposed. Secondly, employing the Lyapunov method and inequality scaling techniques, some sufficient conditions are obtained to guarantee the finite-time synchronization in complex multi-layer networks. Then, we derive estimation expressions for both the convergence time and energy consumption. Furthermore, we establish analytical relationships between the convergence time, energy consumption estimates, and the number of network layers. Finally, numerical simulations are presented to validate the effectiveness of the proposed theoretical approach.