Abstract
In this paper, the finite-time and fixed-time synchronization problems of multi-layer networks are studied. In order to achieve the synchronization, two novel switching controllers are proposed and the effectiveness is verified by the Lyapunov stability theory. Moreover, the upper bound of time and energy costs are estimated. Specifically, the results show that increasing the synchronization speed will inevitably increase the consumption of control energy, which means there is a trade-off between time and energy costs. Therefore, an index function is given to quantify the time and energy costs, and it is found that adjusting the parameters can minimize the total cost. Finally, the theoretical results are verified by some numerical simulations.
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