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This work investigates the synchronization problem of a dynamical network composed of nonlinear nodes with directed couplings and suffering from heterogeneous delays. Specifically, a time-varying pinning control is adopted to achieve synchronization. The system’s dynamics are interpreted under a multiplex network framework, from which an indicator is designed to measure the synchronizability of the pinned network. Criteria are then derived to ensure exponential synchronization while the largest admissible coupling delay is also estimated. These criteria are based on the time average of the proposed indicator over some user-defined time intervals. Therefore, it possesses high versatility to support a wide range of scenarios with different intermittent control strategies. An interesting observation is that the proposed indicator is always upper bounded, manifesting that if the couplings between the nodes are too weak, pinning synchronization may fail no matter how large the pinning gain is. To further demonstrate the applicability of the theorem and the corollaries, numerical examples under different pinning configurations are presented. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization problem for networked nonlinear agents with time-varying control gain is studied under a synchronous periodic data sampling framework. To achieve synchronization, both the state-dependent and time-dependent event-triggered protocols are proposed. The effectiveness of these protocols is justified by Lyapunov stability theorem based on rigorous mathematical proof, facilitated by a delayed differential inequality with time-dependent parameters. Instead of specifying a lower bound for the control gain, as others usually suggested, our criteria rely on its time-average and thus allow higher flexibility in controller design. Numerical simulations are also presented to confirm the reaching of synchronization and demonstrate the wide applicability of the proposed protocols. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problem of nonlinear multi-agent systems with time-varying control in the presence of transmission delay over a communication network. To facilitate the study, a novel delayed differential inequality with time-varying coefficients is first established. Then, the synchronization problem is recast into the stability problem of a delayed differential system with certain time-dependent parameter. A sufficient criterion is further formulated to guarantee the synchronization. The mathematical proof reveals that the time average of the control strength is crucial for reaching synchronization. Together with the agent dynamics and the topology, this average also governs the largest admissible delay. Moreover, the criterion is applied to synchronization problems with general on-off coupling under data sampling and delayed communications, respectively. Some useful corollaries are consequently deduced. Finally, numerical simulations are presented to illustrate the validity of our theoretical results. [ABSTRACT FROM AUTHOR]