Event-Based Prescribed-Time Synchronization of Directed Dynamical Networks With Lipschitzian Nodal Dynamics

This brief investigates the prescribed-time synchronization problem of directed dynamical networks with both weighted edges and identical nodes of Lipschizian nonlinearity. We first establish a novel lemma for prescribed-time stability, then develop an event-triggered control scheme with a time-varying control gain. In our design, all nodes decide their control signals with discretely updated relative states according to a well-designed yet simple triggering condition, and the computational capability and power energy can be mitigated. Meanwhile, synchronization is proved to be achievable within a prescribed time length. Besides, it is shown that the control signals remain bounded despite the increasing control gain, and no Zeno phenomenon occurs during the control process. Finally, a numerical example is given to verify the validity and effectiveness of the theoretical result.