This technical correspondence considers finite-time synchronization of dynamical networks by designing aperiodically intermittent pinning controllers with logarithmic quantization. The control scheme can greatly reduce control cost and save both communication channels and bandwidth. By using multiple Lyapunov functions and convex combination techniques, sufficient conditions formulated by a set of linear matrix inequalities are derived to guarantee that all the node systems are synchronized with an isolated trajectory in a finite settling time. Compared with existing results, the main characteristics of this paper are twofold: 1) quantized controller is used for finite-time synchronization and 2) the designed multiple Lyapunov functions are strictly decreasing. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.

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In this paper, we investigate the cluster synchronization problem for networks with nonlinearly coupled nonidentical dynamical systems and asymmetrical coupling matrix by using pinning control. We derive sufficient conditions for cluster synchronization for any initial values through a feedback scheme and propose an adaptive feedback algorithm that adjusts the coupling strength. Some numerical examples are then given to illustrate the theoretical results.

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